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

It is currently 23 Aug 2014, 05:41

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

A bus from city M is traveling to city N at a constant speed

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 18 Aug 2009
Posts: 305
Followers: 3

Kudos [?]: 83 [3] , given: 9

GMAT Tests User
A bus from city M is traveling to city N at a constant speed [#permalink] New post 07 Nov 2009, 02:23
3
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

37% (03:29) correct 63% (02:12) wrong based on 206 sessions
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A. 48
B. 72
C. 96
D. 120
E. 192

The source is GMATClub's diagnostic test... would look forward to see some innovative approach to this.
Thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Feb 2012, 23:01, edited 1 time in total.
Edited the question
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 31 Aug 2009
Posts: 422
Location: Sydney, Australia
Followers: 6

Kudos [?]: 106 [1] , given: 20

GMAT Tests User
Re: two buses, same speed... head spinning [#permalink] New post 07 Nov 2009, 03:13
1
This post received
KUDOS
Hmmm I did this question a while ago and got it wrong so trying again :)

Rate x time = distance.
For the initial trip lets the distance to the midpoint be represented by P.
EQN1: R x 2 = P

For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:

Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24

EQN2-EQN1 : 0.5R=24
R=48

So the distance is rate x time = 48 x 4 = 192.
ANS = E
2 KUDOS received
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 909
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 15

Kudos [?]: 203 [2] , given: 18

GMAT Tests User
Re: two buses, same speed... head spinning [#permalink] New post 07 Nov 2009, 03:35
2
This post received
KUDOS
Normally I goof up with distance-speed probs, but got this one right.

here, B1 and B2 are coming towards each other at the same speed, so when they meet they MUST have traveled the same distance.
in 2 hours B1 has traveled 2S miles ( let S be the speed )
so, B2 has also traveled 2S miles

So we have a line segment MN having a distance 4S and PM=MN = 2S. Divide this line segment into four parts with each having distance S.

Okay, for the second trip the total time delay is 60 mins=1 hour. Suppose B2(at N) starts early. In this one hour B2 has traveled S miles. At this time B1 will start and both buses will meet at a point which is halfway of the remaining distance(3S) = 3S/2.

Now, 2S (which represents PM) - 3S/2 (second trip's halfway meeting point) = 12 => S=48.
So, total distance = 4S = 4*48 = 192.
Intern
Intern
avatar
Affiliations: CA - India
Joined: 27 Oct 2009
Posts: 46
Location: India
Schools: ISB - Hyderabad, NSU - Singapore
Followers: 9

Kudos [?]: 409 [0], given: 5

Re: two buses, same speed... head spinning [#permalink] New post 07 Nov 2009, 05:45
I am not sure if I am right, but my ans differs from the 2 posted earlier. I think the distance between M and N should be 96.

Facts given: Both buses travel at the same speed. When they leave at exactly same time from M and N respectively, they meet at P in 2 hours. This means the total journey should be taking 4 hours for both of them individually.

Now, one bus leaves 36 min earlier and other one is delayed by 24 min, there is a total gap of 60 min or 1 hour between the two buses. If their meeting point is now shifted by 24 miles, it means their respective speeds are 24 miles an hour. This drives me to a conclusion that the totla distance between M and N should be 4 * 24 = 96 miles.

Please correct me if i'm wrong!!
5 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 18 Aug 2009
Posts: 305
Followers: 3

Kudos [?]: 83 [5] , given: 9

GMAT Tests User
Re: two buses, same speed... head spinning [#permalink] New post 07 Nov 2009, 07:45
5
This post received
KUDOS
kalpeshchopada7 wrote:
I am not sure if I am right, but my ans differs from the 2 posted earlier. I think the distance between M and N should be 96.

Facts given: Both buses travel at the same speed. When they leave at exactly same time from M and N respectively, they meet at P in 2 hours. This means the total journey should be taking 4 hours for both of them individually.

Now, one bus leaves 36 min earlier and other one is delayed by 24 min, there is a total gap of 60 min or 1 hour between the two buses. If their meeting point is now shifted by 24 miles, it means their respective speeds are 24 miles an hour. This drives me to a conclusion that the totla distance between M and N should be 4 * 24 = 96 miles.

Please correct me if i'm wrong!!


Dear Economist and yangsta8, thanks for the new approaches... i still am spinning though ;)
kalpesh, following is the official explanation which I spent some time to understand (24miles in 30mins):

(I didn't know that these questions have their own thread, sorry for repost)
gmat-diagnostic-test-question-79354.html
The buses travel at the same constant speed. It would take one bus to travel 4 hours to cover the distance between the cities M and N (two buses drove for 2 hours each). We need to find the speed of the bus. If the first bus was delayed by 24 minutes and the second one left 36 minutes earlier, it makes the second bus 24+36=60 minutes ahead of the first bus.

The meeting point was 24 miles away on this second day. We know the distance difference between the two meeting points, but we also need to find difference in time those 24 miles were covered. If the second bus drove for 1 hour before the first one departed, each of them had to go for another 1.5 hour to meet (1.5 hour + 1.5 hour + 1 hour). The second bus traveled for 2.5 hours and the first one for 1.5 hour. Therefore the meeting point on the second day was 30 minutes away from that of the previous day.

So the second bus covered 24 miles in 30 minutes, which gives us the speed of the bus, 48 mph. We can calculate the distance as we already know the speed:

4*48=192 miles.
Expert Post
18 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3375

Kudos [?]: 24570 [18] , given: 2680

Re: two buses, same speed... head spinning [#permalink] New post 07 Nov 2009, 08:02
18
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A. 48
B. 72
C. 96
D. 120
E. 192

Distance between the cities d.

First meeting point \frac{d}{2}, as both buses travel at the same constant speed and leave the cities same time they meet at the halfway.

Total time to cover the d 4 hours, as the buses meet in 2 hours.

On the second day first bus traveled alone 1 hour (36min +24min), hence covered 0.25d, and 0.75d is left cover.

They meet again at the halfway of 0.75d, which is 24 miles from \frac{d}{2}:

\frac{d}{2}-24=\frac{0.75d}{2}

d=192

Answer: E.
_________________

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

4 KUDOS received
Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 58 [4] , given: 76089

Re: two buses, same speed... head spinning [#permalink] New post 29 Mar 2011, 19:29
4
This post received
KUDOS
Bunuel wrote:
Distance between the cities d.

First meeting point \frac{d}{2}, as both buses travel at the same constant speed and leave the cities same time they meet at the halfway.

Total time to cover the d 4 hours, as the buses meet in 2 hours.

On the second day first bus traveled alone 1 hour (36min +24min), hence covered 0.25d, and 0.75d is left cover.

They meet again at the halfway of 0.75d, which is 24 miles from \frac{d}{2}:

\frac{d}{2}-24=\frac{0.75d}{2}

d=192


This is the only explanation that made sense to me! Thanks!! +1
3 KUDOS received
SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1691
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 30

Kudos [?]: 285 [3] , given: 36

GMAT Tests User Premium Member Reviews Badge
Re: two buses, same speed... head spinning [#permalink] New post 29 Mar 2011, 20:41
3
This post received
KUDOS
1
This post was
BOOKMARKED
M----------x------ P-----(d-x)--------N

2v + 2v = d


x = 2v (they meet at halfway)

Next day they meet at x - 24 miles from city M

d/2v = 2 -> On day 1

Next day, in 1 hr, B2 travels v distance = d/4 miles, and then it travels (24 miles + d/4) from there for t hrs at speed v where it meets B1 (B1 has also traveled for t hrs by then)

(24+ d/4)/v = (d/2-24)/v

=> 48 = d/2 - d/4

=> d = 4 * 48 = 192

Answer - E
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 20 Oct 2011
Posts: 5
Followers: 0

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

Re: two buses, same speed... head spinning [#permalink] New post 25 Oct 2011, 14:47
Thanks Bunuel.

Your explanation is very clear ... I also has trouble undersatnding the official answer..
Kudos to you!
Expert Post
6 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4668
Location: Pune, India
Followers: 1075

Kudos [?]: 4794 [6] , given: 163

Re: two buses, same speed... head spinning [#permalink] New post 27 Oct 2011, 05:15
6
This post received
KUDOS
Expert's post
gmattokyo wrote:
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

* 48
* 72
* 96
* 120
* 192

The source is GMATClub's diagnostic test... would look forward to see some innovative approach to this.
Thanks!


A little bit of visualization can help you solve this question in a moment. Look at the diagram below. Since they travel at same speed for 2 hrs, point P must be right in the middle of M and N.
Attachment:
Ques3.jpg
Ques3.jpg [ 13.29 KiB | Viewed 5846 times ]

On the return trip, the following is what happens. One bus starts at 11:24 and reaches P at 1:24. The other bus starts at 12:24 and reaches mid way between P and N at 1:24 (in one hour, it covers half of the distance it usually covers in 2 hrs). At 1:24, both buses have a fourth of the total distance between them. They will both cover equal distances and meet at a point which is 1/8th of the total distance from P. This distance is given as 24 miles. Hence total distance = 24*8 = 192 miles
_________________

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
avatar
Joined: 21 Aug 2010
Posts: 209
Followers: 2

Kudos [?]: 13 [0], given: 28

GMAT Tests User
Re: two buses, same speed... head spinning [#permalink] New post 27 Oct 2011, 11:12
Karishma you are a champ :)
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 11 May 2011
Posts: 376
Location: US
Followers: 2

Kudos [?]: 61 [1] , given: 46

Re: two buses, same speed... head spinning [#permalink] New post 27 Oct 2011, 11:33
1
This post received
KUDOS
@Bunuel - Very neat explanation. Kudos to you..!!
_________________

-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 13 May 2011
Posts: 324
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 19

Kudos [?]: 124 [1] , given: 11

GMAT Tests User
Re: two buses, same speed... head spinning [#permalink] New post 09 Dec 2011, 03:39
1
This post received
KUDOS
Fro those of you who are dependent on MGMAT RTD chart (as i am) can try the following:
From the attached chart#2
P=R(T+3/5)-24
P=R(T-2/5)+24
Therefore, R(T+3/5)-24=R(T-2/5)+24
Solving for R, we get Rate=48 m/h
Plug in value in Chart#1: p=96
So, D=192
Attachments

RTD.gif
RTD.gif [ 3.18 KiB | Viewed 5168 times ]

Intern
Intern
User avatar
Joined: 31 Oct 2011
Posts: 47
Location: India
Followers: 0

Kudos [?]: 13 [0], given: 11

Re: two buses, same speed... head spinning [#permalink] New post 19 Dec 2011, 01:46
Good exp by Bunuel :)
_________________

Regards,
Rajesh
Helping hands are anytime better than praying hearts

Kudos ???!@#$$ !!! I just love them ;)

Manager
Manager
avatar
Joined: 26 Apr 2011
Posts: 226
Followers: 0

Kudos [?]: 31 [0], given: 12

GMAT ToolKit User GMAT Tests User
Re: two buses, same speed... head spinning [#permalink] New post 19 Dec 2011, 02:04
quite confusing question but very good explained by bynnel and karishma
thanks to both of you
Intern
Intern
avatar
Joined: 16 Dec 2011
Posts: 49
GMAT Date: 04-23-2012
Followers: 0

Kudos [?]: 0 [0], given: 12

Re: two buses, same speed... head spinning [#permalink] New post 30 Dec 2011, 01:14
good explanation bunuel.......... thanks
Director
Director
avatar
Joined: 28 Jul 2011
Posts: 583
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1

Kudos [?]: 39 [0], given: 16

GMAT Tests User
Re: two buses, same speed... head spinning [#permalink] New post 30 Dec 2011, 06:20
good challenging question and an amazing explanation by karishma
_________________

+1 Kudos If found helpful..

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 178

Kudos [?]: 925 [0], given: 235

GMAT Tests User Reviews Badge
Re: two buses, same speed... head spinning [#permalink] New post 01 Jan 2012, 09:28
suppose total distance = 2d and point p is at d distance from M and N.

for bus M
d+24 = v(1+36/60) = 1.6v

for bus N
d-24 = v(1-24/60) = 0.6v

subtract them, we get v=48

final distance = 2v*t = 4v =192 ( final distance = 2vt because relative speed = v1+v2 = 2v)
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Intern
avatar
Joined: 05 Aug 2011
Posts: 13
Followers: 0

Kudos [?]: 0 [0], given: 6

Re: two buses, same speed... head spinning [#permalink] New post 27 Feb 2012, 22:03
Bunuel wrote:
\frac{d}{2}-24=\frac{0.75d}{2}



why do you assume -24 instead of +24?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3375

Kudos [?]: 24570 [0], given: 2680

Re: two buses, same speed... head spinning [#permalink] New post 27 Feb 2012, 22:36
Expert's post
T740qc wrote:
Bunuel wrote:
\frac{d}{2}-24=\frac{0.75d}{2}



why do you assume -24 instead of +24?


You can derive this either my reasoning or simply by noticing that d/2>0.75d/2, so it should be d/2-24=0.75d/2 (greater value minus 24 equals to smaller value).

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

Re: two buses, same speed... head spinning   [#permalink] 27 Feb 2012, 22:36
    Similar topics Author Replies Last post
Similar
Topics:
Train X traveled 250miles from the city A to the city B. At leokkim 7 27 Jul 2007, 09:34
Car X traveled from city A to city B in 30 minutes. The faifai0714 3 26 Oct 2006, 12:40
A motorist travels from City X to City Y in 2 hours at an desiguy 7 06 Dec 2005, 12:29
Bob travelled 75% of the way from city A to city B by cloudz9 2 04 Jun 2005, 15:33
Marc traveled from city A to city B covering as much christoph 6 02 May 2005, 11:46
Display posts from previous: Sort by

A bus from city M is traveling to city N at a constant speed

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 28 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®.