February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT!
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 184
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
19 Feb 2011, 06:51
Question Stats:
78% (01:32) correct 22% (02:02) wrong based on 2032 sessions
HideShow timer Statistics
Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B? A. 1.5 B. 2.0 C. 2.5 D. 3.0 E. 3.5 I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A Speed of Car B => 20/5850 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58
Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t
As both are moving in the same direction ,both will travel the same distance till catch up time d using this information i created two equations and try to solve but i am not getting correct answer
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The proof of understanding is the ability to explain it.




Math Expert
Joined: 02 Sep 2009
Posts: 52907

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
19 Feb 2011, 07:08
GMATD11 wrote: Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
a)1.5 b)2.0 c)2.5 d)3.0 e)3.5
I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A Speed of Car B => 20/5850 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58
Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t
As both are moving in the same direction ,both will travel the same distance till catch up time d using this information i created two equations and try to solve but i am not getting correct answer Relative speed of car A is 5850=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours. Answer: E. P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 725

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
12 Mar 2011, 09:39
Using relative speed concept  Relative speed = the distance will shrink between the two cars effectively @ 8 miles per hour
Distance to be covered by A = Difference + Lead = 20 + 8 = 28 miles
Time = Distance / Relative Speed = 28 / 8 = 7/2 = 3.5 hrs.
using time distance concept   Let t hrs be the time to overtake
Distance traveled by A = 58t miles = 20 + Distance traveled by B = (20 + 50t)
=> 58t = 50t + 20
t = 2.5 hrs
Let k hrs be the time to cover extra 8 miles by A
Distance traveled by A = 58k miles = 8 + Distance traveled by B in k hrs = (8 + 50k) miles
=>8 + 50k = 58k k = 1.0 hrs
Total time = t + k = 2.5 + 1.0 = 3.5 hrs




Retired Moderator
Joined: 20 Dec 2010
Posts: 1795

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
19 Feb 2011, 09:35
Question says that B gets a head start of 20 miles from A. Say, B traveled x miles when A was already 8 miles ahead of B. Thus, Total distance traveled by B = x miles @ speed 50m/h Total distance traveled by A = 20+x+8 miles @ speed 58m/h ("A" covered the 20m lag; covered the distance x that B covered and got a lead of 8 miles) It is given that they both traveled these distances in the same time/duration; Time spent by B = Time spent by A Time = Distance/Speed x/50 = (20+x+8)/58 58x = 1000+50x+400 8x = 1400 x = 175 miles We know the value of x. We need to find out the time taken by A to travel the distance = 20+x+8 = 20+175+8 = 203miles A traveled the distance of 203 @ 58m/h in 203/58 h = 3.5h. Ans: "E"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 18 Feb 2011
Posts: 2

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
12 Mar 2011, 09:02
Hey everyone, I am having problems with this exercise: OG 12 PS 206 Car A is 20 miles behind Car B, which is travelling in the same direction along the same route as Car A. Car A is traveling at a constant speed of 58 miles per hour and Car B is traveling at a constant speed of 50 miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B? a) 1.5 b) 2.0 c) 2.5 d)3.0 and e)3.5 My approach to this problem was that BOTH cars are moving at the same time, therefore: 1st see how much time it takes to overtake (be on the same place) distance for Car B = 20 + x distance for Car A = x time = distance/rate times are equal hence: (20+x)/58 = x/50 x = 25/2 Car B reaches Car A 37,5 miles ahead. Time for this to happen = (37,50/58) Now for Car B to overtake and drive 8 miles ahead: distance Car A = z + 8 distance Car B= z Assuming it takes them the same time (z+8)/58 = z/50 z = 5 Car B takes 13/58 time to do this. Thereore the total time should be 37,50/58 + 13/58 which is < 1 however the answer on OG states the following explanation: Understand that Car A first as to travel 20 miles behind car B to catch up to car B and then has to travel an additional 8 miles ahead of Car B, a total of 28 extra miles to travel relative to Car B. It can be stated that Car A is traveling 58  50 = 8 miles per hour faster than Car B.
By substitution of the distance/rate = time formula we have : 28 miles/8 miles per hour = 3.5 hoursTHE ANSWER WOULD BE E) 3.5 HOURS. I think this appoach only valid if we DO NOT TAKE in consideration that while Car A is moving Car B is also moving. My question is, where is my mistake on reading the problem? what do you think?



Intern
Joined: 09 Sep 2012
Posts: 17

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
19 Mar 2013, 12:28
Just making some formulas : 1. If Objects move in samedirection : The relative speed can be Added / Substracted . ie. If Car A is moving at X km/hr and Car B is moving at Y km/hr . X > Y imagine car B to be stopped at car A moving at XY km/hr 2. If Objects moving in oppdirection (towards OR away from each other) if If Car A is moving at X km/hr from Left to right And Car B @ Y km/hr from R2L imagine car B stationary and A moving toward it at X+Y kms/hr Eski
_________________
Your Kudos will motivate me :)



Intern
Joined: 20 Mar 2013
Posts: 1

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
20 Mar 2013, 09:01
car a 58mph...car b 50mph..so in 1hour..car goes 8mile ahead..to cover 20mile car a will take 2.5hr..hence an additional 1hour to go 8mile ahead..hence 3.5 in total



Intern
Joined: 19 Feb 2013
Posts: 3

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
16 Apr 2013, 11:26
Bunuel wrote: GMATD11 wrote: Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
a)1.5 b)2.0 c)2.5 d)3.0 e)3.5
I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A Speed of Car B => 20/5850 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58
Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t
As both are moving in the same direction ,both will travel the same distance till catch up time d using this information i created two equations and try to solve but i am not getting correct answer Relative speed of car A is 5850=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours. Answer: E. P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours. Car A need to drive 28 mile, so time for A= 28/58 But as car B is moving too 28/588/50=3 Can you help me, what i am missing?



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1057
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
16 Apr 2013, 11:42
Marchikn wrote: Car A need to drive 28 mile, so time for A= 28/58 But as car B is moving too 28/588/50=3 Can you help me, what i am missing? Hi Marchikn, you are missing the fact that while a "catches up" B is still driving forward. Here is my solution: \(speedA = 58, speedB=50\) this means that every hour A gains \(5850=8\) miles on B. In how many hours will A reach B? space=time*speed, space = distance between cars, speed is the rate at which A is catching up (difference of the speeds AB) \(t=\frac{20}{8}=2.5h\) A will take 2.5 h to reach B. But the question asks "when A will be 8 miles ahead", so we need to add to this time the time it will take A to do so. \(8=t*8\), \(t=1\), 1h to get 8 miles ahead + 2.5 h to reach B = \(3.5h\) Let me know if it's clear.
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8882
Location: Pune, India

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
16 Apr 2013, 23:29
Marchikn wrote: Bunuel wrote: GMATD11 wrote: Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
a)1.5 b)2.0 c)2.5 d)3.0 e)3.5
I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A Speed of Car B => 20/5850 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58
Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t
As both are moving in the same direction ,both will travel the same distance till catch up time d using this information i created two equations and try to solve but i am not getting correct answer Relative speed of car A is 5850=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours. Answer: E. P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours. Car A need to drive 28 mile, so time for A= 28/58 But as car B is moving too 28/588/50=3 Can you help me, what i am missing? The concept being used here is relative speed. Check out my post: http://www.veritasprep.com/blog/2012/07 ... elatively/Time taken by A = 28/(58  50) = 3.5 hrs We subtract 50 because of what you said  B is moving too and B's speed is 50. The concept will be clear once you through the post.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 25 Jan 2013
Posts: 34
Location: Spain
Concentration: Finance, Other

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
17 Apr 2013, 04:18
Let t be time car A needs to overtake car B and drive 8 miles ahead. Then:
58t  20 = 50t + 8
t=28/8=3.5 hours
Hope this helps
Posted from my mobile device



Intern
Joined: 05 May 2014
Posts: 3

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
07 Jun 2014, 03:59
Hi Karishma, I read your document at below: veritasprep/blog/2012/07/quarterwitquarterwisdomspeedingrelatively/ Could you please share the next week doc which is mentioned there for some tougher relative speed questions? "Next week, we will look at some tougher relative speed questions"



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8882
Location: Pune, India

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
08 Jun 2014, 21:59
Nishant1234567 wrote: Hi Karishma, I read your document at below: veritasprep/blog/2012/07/quarterwitquarterwisdomspeedingrelatively/ Could you please share the next week doc which is mentioned there for some tougher relative speed questions? "Next week, we will look at some tougher relative speed questions" Here are two posts discussing relative speed questions: http://www.veritasprep.com/blog/2012/08 ... speeding/http://www.veritasprep.com/blog/2012/08 ... concepts/P.S.  In case you are looking for posts on particular topics, just use the search feature e.g. type "relative speed quarter wit" in the Search field of our blog.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 10 Mar 2013
Posts: 498
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
17 Jun 2014, 01:14
To solve this problem we need to know just the difference in Kilometers between A and B. The difference = 20 Miles + 8 Miles = 28 8*T=28 > T=28/8 = 3,5 E
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Manager
Joined: 15 Aug 2013
Posts: 244

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
12 Aug 2014, 18:19
Bunuel wrote: GMATD11 wrote: Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
a)1.5 b)2.0 c)2.5 d)3.0 e)3.5
I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A Speed of Car B => 20/5850 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58
Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t
As both are moving in the same direction ,both will travel the same distance till catch up time d using this information i created two equations and try to solve but i am not getting correct answer Relative speed of car A is 5850=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours. Answer: E. P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours. Hi Bunuel, Can you please guide me to the location of additional relative rate problems? Thanks!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8882
Location: Pune, India

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
12 Aug 2014, 20:40
I am sure Bunuel will give you a dozen links for practice questions but meanwhile, here are some of my posts with relative speed practice questions: http://www.veritasprep.com/blog/2012/07 ... elatively/http://www.veritasprep.com/blog/2012/08 ... speeding/http://www.veritasprep.com/blog/2012/08 ... concepts/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 06 Jun 2011
Posts: 22

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
25 Oct 2014, 09:16
I've done these problems numerous times but got stuck into a very easy problem in the main exam. I feel that its useful to have a uniform strategy for these two types of these distancetime problems 1. A overtakes B ( using relative speed concept) 2. A is travelling toward B. ( e.g the NYDallas problem).
Thanks to experts' posts.



Intern
Joined: 09 Sep 2015
Posts: 1

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
11 Nov 2015, 18:41
I find it easier to understand by looking at the distances:
lets say distance of car A is (Rate x Time) > 58xTime car B is > 50xTime
So at some Time car A with its 58 miles per hour rate: will manage to cover 20 miles to break even + 8 miles to get ahead
Distance of A = Distance of B +20 +8 58xTime = 50xTime + 28
8Time = 28 Time = 3.5



Intern
Joined: 19 Aug 2015
Posts: 5

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
27 May 2016, 22:37
For every hour car b travels 58 miles and car a travels 50 miles. Therefore, for every 1 mile of car a, car b travels 8 miles every hour. In first hour  car a travel 50 miles, car b travel 58 miles  distance left 20  8 =12 In Second hour  car a travel 100 miles, car b travel 116 miles  distance left 20  16 =4 In third hour  car a travel 150 miles, car b travel 174 miles  distance left 20  24 = 4 (4 km ahead car b has overtaken car a) In fourth hour  car a travel 200 miles, car b travel 232 miles  distance left 20  32 = 12 ( 12 km ahead) Therefore answer is 4>t>3



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
Show Tags
13 Jul 2016, 06:44
GMATD11 wrote: Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
A. 1.5 B. 2.0 C. 2.5 D. 3.0 E. 3.5 We can classify this problem as a “catch up and pass” rate question. This means that one car is catching up to the other car and passing it by some distance. Since there is a change in rate as well as a change in distance between the two cars, we can use the formula: time = (change in distance)/(change in rate) We are given that car A is 20 miles behind car B and we need to determine the time when car A is 8 miles ahead of car B. Thus, we can say that the change in distance is 20 + 8 = 28 miles. We are also given that car A travels at a constant speed of 58 mph and car B travels a constant speed of 50 miles per hour. Thus, we can say that the change in rate is 58 – 50 = 8 mph. We can plug this information into our equation: time = (change in distance)/(change in rate) time = 28/8 = 7/2 = 3.5 hours The answer is E.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
13 Jul 2016, 06:44



Go to page
1 2
Next
[ 31 posts ]



