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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: two buses, same speed... head spinning [#permalink]

Show Tags

27 Feb 2012, 23:45

Bunuel wrote:

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,

do you mind explaining the reasoning? think it'll help me set up similar equations more easily. thanks!

Re: A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

12 Apr 2012, 06:51

Help me please to realize whats wrong with my solution? @what point exactly I'm making a mistake?

form the first part of data i can get (1 bus) X*2=2X (2 bus) X*2=2X -->the total distance is 4X

Taking into account the following assumptions, 1)the 1st bus began to drive later for 24 min 2)both buses have the same rate --> the 1st has to travel less distance than the 2d, since it started to travel later but the second earlier 3)the total distance is 4X i set up two equations: (1 bus) X*(t+24)=2X-24 (2 bus) X*(t-36)=2X+24

since 2X is a half of the distance i can rewrite the two equations: X(t+24)+24=X*(t-36)-24 --->60X=-48 what makes me crazy and i don't know where is the flaw in my logic (excluding the fact, that I'm a woman)

Re: A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

09 Jul 2013, 04:40

Let s be the speed of the buses. Thus total distance betn the two cities is 4s. On the first day, thus they meet P, which is at a distance of 4s/2= 2s from their starting points. The next day , in effect one bus has travelled for 1 hour before the other starts. Distance covered in 1 hour =4s/4= s. Remaining distance is 3s. Point at which the two buses meet now, is at a distance of 3s/2 which is also a distance of 24 from P. Thus, 3s/2 = 2s- 24 or s =48 . therefore distance = 4 * 48 =192.

Re: A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

05 Aug 2013, 11:04

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?

let d=distance (what the question is looking for)

On the first day, bus a and bus b travel at the same constant speed. Because they travel at the same constant speed, when they meet at point P they have each traveled for 2 hours. Therefore, the total time (at that constant speed) from A to B is 4 hours and P is the mid distance between those two points.

On the second day each bus travels at the same constant speed. The bus that leaves first spends a total of one hour on the road before the second bus leaves (if bus a and bus b normally leave at the same time and today one leaves 36 minutes earlier and 24 minutes later respectively)

Here is where I get thrown off (using Bunuel's explanation to structure mine)

The wording is a bit ambiguous (at least to me) regarding the constant speed of bus A and bus B. On the second day, do they travel the same constant speed they did the day before or did they each travel the same constant speed that day that is different from the day before?

If they each traveled at the same rate they did before (which is 1/4 of the distance every hour) and today one bus traveled for an hour before the other set off, then today one bus traveled .25d of the way

(d/2) - 24 = (.75d/2)

(I'm not sure as to why that is)

Maybe this is why:

(d/2) represents the speed each bus travels and the midpoint at which bus A and B meet on the first day. (d/2)-24 would represent the bus reaching a point 24 miles before the midpoint. This is equal to a distance that's 3/4ths normal???? Help!!!

Bunuel, I read the link you posted offering an explanation of how that formula represents the point at which each bus meets the second day but I am still confused. Why is the halfway .75d?

Here is another way to look at it. Let's say bus A starts first and B, second. When bus A travels one hour bus B starts. When bus A has traveled for two hours, bus B has traveled for one. When bus A and B meet, A has been on the road for 2.5 hours and B, for 1.5 at a place 24 miles away from the mid distance of the journey.

We can break the journey up into four identical blocks, each representing an hour long portion of the journey (see attached image) when bus A and B meet they meet in the exact middle of one of those 4 identical blocks meaning that 24 miles represents 1/2 of one block. This means there are two 24 mile portions in each of the four blocks. 2*24*4=192.

Re: two buses, same speed... head spinning [#permalink]

Show Tags

31 Dec 2013, 06:18

2

This post received KUDOS

Bunuel wrote:

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,

Here's the way I did it. Let's call X the total distance

Let's focus on the second part of the problem

One bus had a head start of 1 hour. In that hour we traveled 1/4 of the distance. (Since he traveled 1/2 of the distance in 2 hours from question stem)

Now, there are 3/4x of the distance to be traveled

Since they both have the same rate, they will meet at half the distance of 3/4x, so they will meet at 1/4x + (3x/4/2) = 5/8x

Now remember from the first part of the question that point P is exactly the mid point (Same rates, same time)

So we are now at point 5/8x. The question also says that this distance is equal to 24 miles.

So we have 5/8x - 1/2x =1/8x = 24 miles

And so, we get 24*8 = 192 miles for the total distance 'x'

Re: A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

17 Jan 2015, 23:46

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

12 Oct 2015, 14:12

1

This post was BOOKMARKED

R=speed of each bus 2R=distance from each city to P 4R=distance between two cities bus1 distance to meeting 2nd day=2R+24 bus2 distance to meeting 2nd day=4R-(2R+24)=2R-24 2R+24-(2R-24)=48 miles bus1 drives 48 miles more than bus2 in 1 extra hour R= 48 mph 4R=192 miles distance between two cities

Last edited by gracie on 03 Apr 2016, 11:10, edited 1 time in total.

A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

19 Dec 2015, 05:58

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?

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!

I just don't know, why my brain is in the standby mode during the cat, now I've solved this one very quickly ~ 1m 20sec ))) P is the midpoint or Total \(\frac{Distance}{2}\), so one of them have traveled 24 miles more than the half of the distance, and guess which bus has made it (the one, that started his trip 36+24=60 min earlier, let's say it was Bus B) Bus A:\(r*t=p-24\) Bus B \(r*(t+1)=p+24\) => \(r*t+24=r*(t+1)-24\) Rate = 48, so if each of them traveled 2 hours on the first day, than the whole distance can be covered in 4 hours by each of them --> \(4*48=192\) Answer 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 !

The reason you can write (1) is because d/4 was already covered by Bus A before even Bus B started, and half of the remaining distance was covered together by both buses. So total distance covered by Bus A (which traveled for an hour more) is exceeding there previous mid point by 24mi

If you see both Bunuel's and above explanation, simplify to the common solution.

Re: A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

16 Mar 2016, 04:45

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?

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!

Let the distance be 4x Together they take 4 hours to meet at constant speed. In the first case they meet at the mid point. In the second case, one bus start 1 hour earlier than the other. So, it must have covered x distance. In the remaining distance of 3x, each bus covers 1.5x It implies one bus covers 2.5x and another 1.5x That is from the mid point .5x distance, which is given as 24 miles. Therefore, total distance is 8*24=192 miles

A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

03 Apr 2016, 08:15

1

This post was BOOKMARKED

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?

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!

I think this could be solved with the help of relative speed & unitary method concept: Since speed of both the bus is the same, let's assume it as "X" Moving in opposite direction (with same speed), gives the relative speed as 2x

In 1 hour (24 min + 36 min), distance moved from point P = 24 miles Using unitary method, For relative speed 2x, distance moved = 24 miles (i.e. each bus reduced the distance by 24 miles) Therefore, total distance moved by both bus = 24 miles + 24 miles = 48 miles (in 1 hour)

In 4 hours the distance travelled = 48*4 = 192 Miles

Re: A bus from city M is traveling to city N at a constant speed [#permalink]

Show Tags

06 Apr 2017, 23:05

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...