Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Jul 2014, 17:29

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Car B starts at point X and moves clockwise around

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
User avatar
Joined: 24 Sep 2009
Posts: 107
GMAT 1: 710 Q49 V37
Followers: 1

Kudos [?]: 21 [2] , given: 25

GMAT Tests User Reviews Badge
Car B starts at point X and moves clockwise around [#permalink] New post 26 Feb 2012, 21:51
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

47% (03:39) correct 53% (02:42) wrong based on 240 sessions
Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

A. 4pi – 1.6
B. 4pi + 8.4
C. 4pi + 10.4
D. 2pi – 1.6
E. 2pi – 0.8
[Reveal] Spoiler: OA
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18832
Followers: 3267

Kudos [?]: 22816 [5] , given: 2651

Re: Car B starts at point X and moves clockwise around... [#permalink] New post 26 Feb 2012, 22:13
5
This post received
KUDOS
Expert's post
NYCAnalyst wrote:
Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

A. 4pi – 1.6
B. 4pi + 8.4
C. 4pi + 10.4
D. 2pi – 1.6
E. 2pi – 0.8


Step by step analyzes:

B speed: 2 mph;
A speed: 3 mph (travelling in the opposite direction);
Track distance: 2*\pi*r=20*\pi;

What distance will cover B in 10h: 10*2=20 miles
Distance between B and A by the time, A starts to travel: 20*\pi-20

Time needed for A and B to meet distance between them divided by the relative speed: \frac{20*\pi-20}{2+3}= \frac{20*\pi-20}{5}=4*\pi-4, as they are travelling in opposite directions relative speed would be the sum of their rates;

Time needed for A to be 12 miles ahead of B: \frac{12}{2+3}=2.4;

So we have three period of times:
Time before A started travelling: 10 hours;
Time for A and B to meet: 4*\pi-4 hours;
Time needed for A to be 12 miles ahead of B: 2.4 hours;

Total time: 10+4*\pi-4+2.4=4*\pi+8.4 hours.

Answer: B.

Also discussed here: rates-on-a-circular-track-86675.html#p849908

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4593
Location: Pune, India
Followers: 1041

Kudos [?]: 4547 [4] , given: 162

Re: Car B starts at point X and moves clockwise around [#permalink] New post 27 Feb 2012, 04:51
4
This post received
KUDOS
Expert's post
NYCAnalyst wrote:
Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

A. 4pi – 1.6
B. 4pi + 8.4
C. 4pi + 10.4
D. 2pi – 1.6
E. 2pi – 0.8


It is a long question stem so make sure you analyze each statement as you read it otherwise you will waste a lot of time re-reading the question again and again. Let me tell you how:

Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph.

Ok, car B covers 2 miles every hour moving clockwise. We don't know the track length yet.

Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph.
Car A is faster and covers 3 miles every hour counter clockwise. Since their directions are opposite, their relative speed = 2+3 = 5 mph. We still don't know the track length so we cannot say where car B was when car A started. All we know is that in 10 hrs, car B traveled 20 miles

If the radius of the track is 10 miles,

Now we know the track length. It is 2{\pi}r = 2{\pi}*10 = 20{\pi}. It is greater than 20 miles that car B covered in 10 hrs so car B had not finished one round. Of the 20{\pi}, it had covered 20 miles.

for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?


To pass each other for the first time, cars A and B together need to cover the remaining distance on the circle i.e. 20{\pi} - 20. To create a distance of another 12 miles, they together need to travel 12 miles more away from each other

Time taken = Total distance to be traveled/ Relative Speed
Time taken = (20{\pi} - 20 + 12)/5 = (20{\pi} - 8)/5 hrs = 4{\pi} - 1.6 hrs
Car B must have been traveling for 4{\pi} - 1.6 + 10 = 4{\pi} + 8.4 hrs

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18832
Followers: 3267

Kudos [?]: 22816 [0], given: 2651

Re: Car B starts at point X and moves clockwise around [#permalink] New post 27 Feb 2012, 08:47
Expert's post
pbull78 wrote:
Time needed for A to be 12 miles ahead of B: ;
( not understood this bunuel , can u explain ?)

thanks


Since A and B are travelling in opposite directions then their relative speed (2+3) mph. Now, in order the distance between them to be 12 miles, after they pass each other, they should travel for time=distance/rate=12/(2+3)=2.4 hours.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 28 Feb 2012
Posts: 22
GMAT 1: 700 Q48 V39
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 8 [0], given: 3

Re: Car B starts at point X and moves clockwise around [#permalink] New post 28 Feb 2012, 20:45
NYCAnalyst wrote:
Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

A. 4pi – 1.6
B. 4pi + 8.4
C. 4pi + 10.4
D. 2pi – 1.6
E. 2pi – 0.8



My solution -
Let us assume they meet at time t. Till that time, Car B will have travelled a distance of 2t (distance = speed *time).
Car A will have travelled a distance equal to (t-10)*3 by the same logic.
So, we have
2t + (t-10)*3 = 2 * pi * 10 (at t )

For putting in another 12 miles between them,

2t + (t-10)*3 = 2 * pi * 10 + 12
which gives
2t + 3t - 30 = 20*pi+12
5t - 30 = 20*pi +12
5t = 20*pi + 42
t = 4*pi + 8.4 (Answer B)

- Deepti
Director
Director
avatar
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 12

Kudos [?]: 295 [0], given: 217

GMAT Tests User
Cars on circular track [#permalink] New post 03 Mar 2012, 14:18
Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

A) 4pi – 1.6
B) 4pi + 8.4
C) 4 pi+ 10.4
D) 2 pi – 1.6
E) 2pi – 0.8


This is how I tried solving this, but got stuck after this.

The two cars travel around the circumference of a circle, the measure of which is 2 pi r = 2 pi × 10 = 20 pi miles.

Car B has already traveled (2 mph)(10 hours) = 20 miles in a clockwise direction by the time Car A starts moving 10 hours later in a counterclockwise direction (and from the same starting point).

At Car A’s start time, the additional distance to cover before the cars meet is (20pi – 20) miles. We are interested in the moment when the cars have passed each other and have traveled another 12 miles: (20 pi – 20) + 12 = (20 pi – 8) miles.

No idea what to do after this.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

Manager
Manager
avatar
Joined: 29 Sep 2008
Posts: 154
Followers: 2

Kudos [?]: 20 [0], given: 1

GMAT Tests User
Re: Car B starts at point X and moves clockwise around [#permalink] New post 18 Apr 2012, 01:29
i don't know where i am making the mistake ...

Car B has already traveled (2 mph)(10 hours) = 20 miles in a clockwise direction by the time Car A starts moving 10 hours later in a counterclockwise direction (and from the same starting point).

let x distance from Car A starting point the two cars meet

then distance covered by car B=2pi*10-20-x
time taken by car B=(2pi*10-20-x)/2
distance covered by car A=x
time taken by car A=x/3

equating the two,
x/3=(2pi*10-20-x)/2
2x=60*pi-60-3x
x=(60*pi-60)/5
x=12(pi-1)
car B has to travel another 12 miles,therefore time taken by car B=(2pi*10-20-x+12)/2

or (20*pi-8-12*pi+12)/2=4*pi+2
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18832
Followers: 3267

Kudos [?]: 22816 [0], given: 2651

Re: Car B starts at point X and moves clockwise around [#permalink] New post 18 Apr 2012, 03:33
Expert's post
mrinal2100 wrote:
i don't know where i am making the mistake ...

Car B has already traveled (2 mph)(10 hours) = 20 miles in a clockwise direction by the time Car A starts moving 10 hours later in a counterclockwise direction (and from the same starting point).

let x distance from Car A starting point the two cars meet

then distance covered by car B=2pi*10-20-x
time taken by car B=(2pi*10-20-x)/2
distance covered by car A=x
time taken by car A=x/3

equating the two,
x/3=(2pi*10-20-x)/2
2x=60*pi-60-3x
x=(60*pi-60)/5
x=12(pi-1)
car B has to travel another 12 miles,therefore time taken by car B=(2pi*10-20-x+12)/2

or (20*pi-8-12*pi+12)/2=4*pi+2


What does the red part even mean? If it means the distance between B and A by the time, A starts to travel then we know exactly what it is. It equal to: 20*\pi-20 (car-b-starts-at-point-x-and-moves-clockwise-around-128215.html#p1050349).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 29 Sep 2008
Posts: 154
Followers: 2

Kudos [?]: 20 [0], given: 1

GMAT Tests User
Re: Car B starts at point X and moves clockwise around [#permalink] New post 18 Apr 2012, 04:28
i have explained the statement marked in red "let x distance from Car A starting point the two cars meet" by means of diagram.Both the cars meet at the point.Car A travels x mile while car B travels a distance of 2pi*10-20-x.Since the time taken would be equal,we are equating the equation

x/3=(2pi*10-20-x)/2
Attachments

File comment: diagram
car pblm.docx [65.79 KiB]
Downloaded 43 times

To download please login or register as a user

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4593
Location: Pune, India
Followers: 1041

Kudos [?]: 4547 [0], given: 162

Re: Car B starts at point X and moves clockwise around [#permalink] New post 18 Apr 2012, 09:24
Expert's post
mrinal2100 wrote:
i don't know where i am making the mistake ...

Car B has already traveled (2 mph)(10 hours) = 20 miles in a clockwise direction by the time Car A starts moving 10 hours later in a counterclockwise direction (and from the same starting point).

let x distance from Car A starting point the two cars meet

then distance covered by car B=2pi*10-20-x
time taken by car B=(2pi*10-20-x)/2
distance covered by car A=x
time taken by car A=x/3

equating the two,
x/3=(2pi*10-20-x)/2
2x=60*pi-60-3x
x=(60*pi-60)/5
x=12(pi-1)


Everything is correct till here. Now, x is the distance traveled by A so time taken = x/3 = 12(pi-1)/3 = 4(pi-1)

Now notice that they have to together put 12 miles distance between them. They are moving in opposite directions so time taken to cover 12 miles together = 12/(2+3) = 2.4 hrs (relative speed concepts)

Total time taken = 4(pi-1) + 2.4 = 4*pi - 1.6 hrs
Car B has traveled 10 hrs extra so it must have been traveling for 4*pi - 1.6 + 10 = 4*pi + 8.4 hrs
car B has to travel another 12 miles,therefore time taken by car B=(2pi*10-20-x+12)/2
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
User avatar
Joined: 07 Sep 2011
Posts: 65
Location: United States
Concentration: Strategy, International Business
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Followers: 3

Kudos [?]: 26 [0], given: 3

Re: Car B starts at point X and moves clockwise around [#permalink] New post 18 Apr 2012, 21:32
Hi Karishma,

I have been fan of your logical approach, which I keep applying wherever possible. More so when I am not very comfortable with algebra part of word problems. I am attempting to solve this question based on logic.

I will consider Pi as 3. So the distance round the circle is 20pi or 60 mi approx.
Out of this Car B has already traveled 20 mi in 10 hours. Thus we are left with 40 mi to be covered by A and B together but driving in opposite direction @ 3km/hr and 2km/hr respectively. Thus to cover balance distance plus 12km i.e. 52miles, I need 52/5=10.4 hours.

Thus answer is 10hours plus 10.4 hours i.e. 20.4 hours and answer choice B (4pi+8.4) is correct.
Intern
Intern
avatar
Joined: 03 Aug 2011
Posts: 46
Followers: 1

Kudos [?]: -8 [0], given: 17

Re: Car B starts at point X and moves clockwise around [#permalink] New post 13 May 2012, 02:29
I think there is a flaw in this question...

moving on a circular track could not be CONSTANT RATE! it has variable velocity So you could not solve the problem with Rate= Distance/ time Formula. Because this formulation is just for straight distances not for circular ones...
_________________

Keep your eyes on the prize: 750

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4593
Location: Pune, India
Followers: 1041

Kudos [?]: 4547 [0], given: 162

Re: Car B starts at point X and moves clockwise around [#permalink] New post 14 May 2012, 07:58
Expert's post
manjeet1972 wrote:
Hi Karishma,

I have been fan of your logical approach, which I keep applying wherever possible. More so when I am not very comfortable with algebra part of word problems. I am attempting to solve this question based on logic.

I will consider Pi as 3. So the distance round the circle is 20pi or 60 mi approx.
Out of this Car B has already traveled 20 mi in 10 hours. Thus we are left with 40 mi to be covered by A and B together but driving in opposite direction @ 3km/hr and 2km/hr respectively. Thus to cover balance distance plus 12km i.e. 52miles, I need 52/5=10.4 hours.

Thus answer is 10hours plus 10.4 hours i.e. 20.4 hours and answer choice B (4pi+8.4) is correct.


Yes, that's absolutely fine. I followed the exact same approach above (but with pi). I hope you understand that the approximation of pi worked because the answer was also in terms of pi. If you had a pure numerical answer, you would not have assumed pi = 3. Here, pi acted like a variable. Say, if you put pi = 10, you will still get the answer (of course you will need to substitute pi = 10 in the options too)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4593
Location: Pune, India
Followers: 1041

Kudos [?]: 4547 [1] , given: 162

Re: Car B starts at point X and moves clockwise around [#permalink] New post 14 May 2012, 08:02
1
This post received
KUDOS
Expert's post
omidsa wrote:
I think there is a flaw in this question...

moving on a circular track could not be CONSTANT RATE! it has variable velocity So you could not solve the problem with Rate= Distance/ time Formula. Because this formulation is just for straight distances not for circular ones...


Velocity has two components - speed and direction. Velocity is variable here only because of changing direction.

Speed = Distance/Time is applicable for circular distances as well since speed is not a vector.

GMAT only deals with speed, not with velocity. Constant rate implies a constant speed.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
User avatar
Joined: 07 Sep 2011
Posts: 65
Location: United States
Concentration: Strategy, International Business
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Followers: 3

Kudos [?]: 26 [0], given: 3

Re: Car B starts at point X and moves clockwise around [#permalink] New post 16 May 2012, 01:12
Thanks Karishma,

Yes I understand the implication of actual value of pi.
Senior Manager
Senior Manager
avatar
Joined: 05 Sep 2010
Posts: 477
Followers: 1

Kudos [?]: 61 [0], given: 17

Premium Member
Re: Car B starts at point X and moves clockwise around [#permalink] New post 11 Jul 2012, 19:13
"for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them"
i have a little problem with the language of the question stem ..isint the question asking that we have to calculate the time of travel since they met for the first time and to the point when the distance between them is 12 miles .in that case the answer wud have been straight 12 /5 hrs . i feel the language is little faulty .karisma ,buneul plz claify
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4593
Location: Pune, India
Followers: 1041

Kudos [?]: 4547 [0], given: 162

Re: Car B starts at point X and moves clockwise around [#permalink] New post 11 Jul 2012, 20:29
Expert's post
aditya8062 wrote:
"for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them"
i have a little problem with the language of the question stem ..isint the question asking that we have to calculate the time of travel since they met for the first time and to the point when the distance between them is 12 miles .in that case the answer wud have been straight 12 /5 hrs . i feel the language is little faulty .karisma ,buneul plz claify


The language of the question isn't very good. This does lead to different interpretations by different people sometimes. But most people will interpret it as 'from the starting point to right now (which is the point when the cars have passed each other for the first time and put another 12 miles between them)'


In GMAT, the language is always very clear. e.g. you could be given "After some time, the cars had put a distance of 12 miles between them after meeting for the first time. For how many total hrs did car B travel till this time?" - In this case, your answer is the one given above.

or you could have "After meeting for the first time, the cars continued on their respective paths and put a distance of 12 miles between them (they have met only once). How long has car B been traveling since meeting car A for the first time?" - In this case, your answer is 12/5
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 479 [0], given: 43

GMAT Tests User
Re: Car B starts at point X and moves clockwise around [#permalink] New post 11 Jul 2012, 20:50
NYCAnalyst wrote:
Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

A. 4pi – 1.6
B. 4pi + 8.4
C. 4pi + 10.4
D. 2pi – 1.6
E. 2pi – 0.8


It is easier to understand the question using a drawing:

A_1 and B_1
are the points A and B are respectively after their first time pass. If we denote by T the time B travels from X to B_1, then the total distance the two cars travel until the situation depicted in the figure is one whole circumference of the circle plus the overlap of 12 miles. Car A travels T-10 hours.
We can write the following equation:
2T+3(T-10)=2\pi10+12
or 5T=20\pi+42,
from which we get T=4\pi+8.4.

Answer: B
Attachments

CircleMotion-4GC.jpg
CircleMotion-4GC.jpg [ 12.14 KiB | Viewed 6449 times ]


_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 11 Jul 2012
Posts: 46
Followers: 0

Kudos [?]: 0 [0], given: 0

Car B starts at point X and moves clockwise around a circular tr [#permalink] New post 23 Sep 2012, 00:21
Let rA and rB denote the speeds of A and B, respectively
rA = 3mph, rB= 2mph
C = 20*π miles (circumference of the circle)
In 10h B will have covered 20 miles (10h * 2mph)
The remaining distance 20*π - 20 miles and an extra 12 miles (20*π -8 ) got to be covered both by A and B with relative
speed of 5mph.
Thus B will have been racing a total time of 10h + ((20*π -8 )/5) h = 4*π + 8.4 hours
Brother Karamazov
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18832
Followers: 3267

Kudos [?]: 22816 [0], given: 2651

Re: Car B starts at point X and moves clockwise around [#permalink] New post 15 Jul 2013, 00:02
Expert's post
Re: Car B starts at point X and moves clockwise around   [#permalink] 15 Jul 2013, 00:02
    Similar topics Author Replies Last post
Similar
Topics:
A car starts from X and moves towards Y. At the same time SravnaTestPrep 9 29 Aug 2013, 03:15
9 Experts publish their posts in the topic Three bodies A, B and C start moving around a circular track Bluelagoon 12 27 Apr 2012, 13:07
28 Experts publish their posts in the topic Car B begins moving at 2 mph around a circular track with yangsta8 29 11 Nov 2009, 01:34
Experts publish their posts in the topic 2 cars started at the same point and travelled a straight bmwhype2 6 08 Feb 2008, 04:41
A, B and C run around a circular track starting from the kyatin 3 23 Mar 2007, 15:00
Display posts from previous: Sort by

Car B starts at point X and moves clockwise around

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 21 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.