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A bus from city M is traveling to city N at a constant speed while ano 15 Jun 2017, 09:22
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gmattokyo
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!
Show more

Hi..
Q can be solved by taking it the following way..
Since it is constant speed let's take that only one bus travels from m to N.. so that bus will take 2*2=4 hrs..

Now in SECOND case 24 minutes delay and 36 minutes early means difference of 24+36=60 min or 1 HR..
So remaining distance will be covered in 4-1=3 HR..
The remaining distance will be travelled half way that is 3/2 HR by each bus. So the bus which has traveled 1 HR already travels another 1.5 HR.. so total 2 1/2 HR..
But P is half way or 2 hrs away..
Therefore the new point is 2 1/2-2=1/2 HR away..
This 1/2 HR means 24 miles ..
So total distance of 4 hrs corresponds to 4/(1/2) *24=8*24=192 miles
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A bus from city M is traveling to city N at a constant speed while ano Updated on: 11 Jul 2019, 05:58
Originally posted by BrentGMATPrepNow on 08 Dec 2017, 09:23.
Last edited by BrentGMATPrepNow on 11 Jul 2019, 05:58, edited 1 time in total.
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gmattokyo
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
Show more

Buses traveling at SAME speeds meet in point P after driving for 2 hours.
IMPORTANT: Since the 2 buses are traveling at the SAME speed, then point P must be HALF WAY between city M and city N

Also recognize that the TOTAL travel time = 4hrs (2 hrs for each bus)

TOTAL distance traveled = (distance one bus traveled) + (distance other bus traveled)
Distance = (travel time)(rate)
Let r = the rate that EACH bus is traveling.
So, we get: TOTAL distance traveled = 2r + 2r = 4r
So, from the above fact, the distance from point P to city M (and to city N) = 4r/2 = 2r

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?
Another way to read this is: One bus leaves its city. ONE HOUR LATER, the other bus leaves its city.
Let's say Bus A leaves city M at noon, and Bus B leaves city N at 1pm.
Let t = Bus A's travel time until they meet
So, Let t-1 = Bus B's travel time until they meet

Since the TOTAL travel time = 4hrs, we can write: t + (t-1) = 4
Solve to get: t = 2.5
So, Bus A traveled for 2.5 hours, Bus B traveled for 1.5 hours,
This means Bus A traveled further. In fact, Bus A travels PAST point P (which is halfway between cities M and N) for an ADDITIONAL 24 miles
In other words, Bus A's travel distance = 2r + 24
Since Bus A traveled for 2.5 hours at a rate of r, we can write: 2.5r = 2r + 24
Multiply both sides by 2 to get: 5r = 4r + 48
Solve: r = 48

TOTAL distance traveled = 4r
= 4(48)
= 192

Answer: E

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Brent
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A bus from city M is traveling to city N at a constant speed while ano 05 Apr 2020, 11:31
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EMPOWERgmatRichC

any suggestion for testing the answer here?
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A bus from city M is traveling to city N at a constant speed while ano 05 Apr 2020, 20:10
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Camach700
EMPOWERgmatRichC

any suggestion for testing the answer here?
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Hi, Camach700,

YES - you can TEST THE ANSWERS here, but before you start doing that work, you have to hash out all of the information that the prompt gives you to work with. We're given a number of facts in this wordy prompt (and I'm going to summarize the information into my own words):

1) Bus A and Bus B are approaching each other while they each drive at the same constant speed. The buses are both driving the same route.
2) The buses meet at point P after driving for 2 hours each.
3) The following day the buses do the return trip at the same constant speed. One bus (Bus A) is delayed 24 minutes and the other (Bus B) leaves 36 minutes earlier.
4) The NEW meeting point is 24 miles from point P

We're asked for the distance between the two cities.

To start, the 24-minute delay for one bus (Bus A) and a 36-minute early-start for the second bus (Bus B) means that Bus B travels for 1 hour MORE than Bus A does. That 1-hour "head start" has to move the MEETING POINT 24 miles. You might assume that the busses were moving 24 miles/hour, but that would NOT be correct; keep in mind that BOTH Buses will still be moving when they meet (so that 24-mile difference still has to accommodate 2 moving busses)....

Let's start by TESTing one of the larger Answers....

Answer C: 96 miles.

IF... the two buses met after 2 hours of travel, then the 4 total hours of travel would have covered 96 miles and Point P is at the 48-mile 'mark.'
D = (R)(T)
96 miles = (R)(4 hours)
96/4 = 24 miles/hour = R

On the second day, Bus B has a head start, so it travels 24 miles before Bus A gets going. Thus, the two buses would then have to travel the remaining 96-24 = 72 total miles together at 24 miles/hour each. Each hour, the TOTAL distance traveled would be 48 miles.... 72/48 = 1.5 total hours of travel, so each bus would travel 1.5 hours.

In this situation, the buses meet after Bus A has traveled 1.5 hours at 24 miles/hour.... (1.5)(24) = 36 miles.... the 36-mile 'mark.' This is NOT 24 miles away from point P.... it's only 48 - 36 = 12 miles away. This is exactly HALF the distance that it needs to be.... so I'd look to DOUBLE the total distance...

Let's TEST Answer E: 192 miles

IF... the two buses met after 2 hours of travel, then the 4 total hours of travel would have covered 192 miles and Point P is at the 96-mile 'mark.'
D = (R)(T)
192 miles = (R)(4 hours)
192/4 = 48 miles/hour = R

On the second day, Bus B has a head start, so it travels 48 miles before Bus A gets going. Thus, the two buses would then have to travel the remaining 192 - 48 = 144 total miles together at 48 miles/hour each. Each hour, the TOTAL distance traveled would be 96 miles....144/96 = 1.5 total hours of travel, so each bus would travel 1.5 hours.

In this situation, the buses meet after Bus A has traveled 1.5 hours at 48 miles/hour.... (1.5)(48) = 72 miles.... the 72-mile 'mark.' This is 96 - 72 = 24 miles from Point P, so this MUST be the answer.

Final Answer:
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E

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A bus from city M is traveling to city N at a constant speed while ano 18 May 2020, 20:06
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gmattokyo
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!
Show more

I named the buses A and B. Let us refer to the diagram below:

Attachment:
tsd q.png
tsd q.png [ 15.79 KiB | Viewed 4772 times ]

Let speed of each bus = s miles/hr
=> total distance = 2s + 2s = 4s miles

Let P = original meeting point - midpoint of MN - say they would have met at 12:00 if they started together
P' = New meeting point when they started at different times (one early and the other late)

In the return journey: (in the diagram, scenario 3)
B was 36 min early and A was 24 min late => To simplify, let us just assume that B was 60 min early ans A was on time
Since their usual meeting time at P was supposed to be 12 noon, what actually happened is:

B reached P already at 11:00 (1 hour earlier) and then A was possibly at some point P" (at 11:00 am)
He would have taken 1 more hour to reach P (if he actually managed to do so); implying that the distance P-P" = 1 x s = s miles

However, the buses meet at the point P'.
Since both buses have same speeds, P' must be midway between P and P"

=> Distance P-P' = Distance P"-P' = s/2 miles

But P-P' = 24 miles (given) => s/2 = 24 => s = 48

=> Distance MN = 4s = 192 miles
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A bus from city M is traveling to city N at a constant speed while ano 14 Jul 2020, 03:21
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gmattokyo
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!
Show more

It takes 4 hours for each bus to travel the whole distance.

In the second trip, the bus that starts early travels for 1 hour before the other bus starts and so covers 1/4 of the distance.

Then the other bus starts and each travels (3/4)/2 = 3/8 of the distance.

The bus that started early totally travelled 1/4 + 3/8= 5/8 of the total distance

We know that 5/8-1/2 of the total distance = 24 miles

Total distance = 24*8 = 192 miles

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A bus from city M is traveling to city N at a constant speed while ano 29 Aug 2020, 23:18
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call the 1st Bus A leaving from City M to City N

call the 2nd Bus B leaving from City N to City M

Let the Gap Distance between the 2 Buses (and thus the 2 Cities) = d


The Key Fact is that they travel the Same Speed.

After 2 hours they meet at point P. Since they are both traveling over the Same Time (Time is Constant) and they have the Same Speed (their Ratio of Speeds = 1 : 1) ---- they each will travel 1/2 of the Total Gap Distance between them when they meet at Point P.

Thus, the Mile Marker at Point P will = 1/2 * d

Speed of A = can travel 1/2 * d in 2 hours = 1/2d / 2 = d/4
Speed of B = Speed of A = d/4


Now they each have made it to the opposite City they were heading towards and are coming back on the round-trip.

Let Bus B be the bus that is delayed 24 minutes. This means Bus A is the other bus that leaves 36 minutes earlier.

Thus, the Total Head Start that Bus A gets is 1 hour. In 1 hour at the Speed of d/4, Bus A will have covered 1/4th of the total Gap Distance = 1/4*d

Now, when Bus B is ready to leave, there is only 3/4 of d remaining between them. Again, since Both buses run at the Same Speed, they will meet at the half way point. Thus, they will meet after each traveling = (3/4*d) * 1/2 = 3/8*d

Since A already traveled 1/4*d when he had the head-start, A will have traveled a Total of ---- 3/8*d + 1/4*d = 5/8*d. This is the New Mile Marker Point that the 2 buses Meet at (Call it Point Q)


Point Q is at mile marker 5/8*d away from City N where A started on the 2nd Day.
Point P is at mile marker 1/2*d away from City N where B started on the 1st Day.

We are told that when they meet at Point Q on the 2nd Day, that this is 24 miles away from Point P on the 1st Day.

Point Q - Point P = 5/8*d - 1/2*d = 5/8d - 4/8d = 1/8d = 24 miles distance between the 2 Points

1/8*d = 24

d = 24 * 8 = 192 miles

The entire distance between the 2 Cities = 192 miles

A.C. -E-
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A bus from city M is traveling to city N at a constant speed while ano 22 Jan 2021, 06:46
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Bunuel,

Could you please advise whether there is a variation of this question for additional practice?
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A bus from city M is traveling to city N at a constant speed while ano 22 Jan 2021, 07:07
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Bunuel,

Could you please advise whether there is a variation of this question for additional practice?
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A bus from city M is traveling to city N at a constant speed while ano 04 Dec 2021, 14:30
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Since the buses were going the same rate over the same time, they must have traveled the same distance.

Since the sum of the distances is the total distance, D, each then traveled D/2 over 2 hrs, the location of point P.

Each buses rate is then (D/2)/2 = D/4 mph.

The next day one bus started effectively 1 hr before the other, 36 min early + 24 min delay.

The first bus then had traveled D/4 * 1 hr before the second bus started.

Using the same logic from the first day, each bus started then (3/4)D apart and therefore met in the middle, (3/8)D.

This point is 24 miles from point P.

Since point P is D/2 or 4D/8 and the point on the second day is 3D/8, the difference between these two, D/8,= 24 miles as stated.

Therefore D/8=24 and D=192

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A bus from city M is traveling to city N at a constant speed while ano 08 Feb 2022, 09:16
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Hi All,

I am having trouble understanding the language: "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?"

The 24 min delay and the 36mins are relative to what??? For example, it says "the other leaves 36min earlier"... earlier than Bus 1 or earlier than Bus 2 usually does??

This isn't a problem from the OG, is it??
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A bus from city M is traveling to city N at a constant speed while ano 09 Feb 2022, 23:01
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GK002
Hi All,

I am having trouble understanding the language: "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?"

The 24 min delay and the 36mins are relative to what??? For example, it says "the other leaves 36min earlier"... earlier than Bus 1 or earlier than Bus 2 usually does??

This isn't a problem from the OG, is it??
Show more

GK002

It is implied that they both start at the same time on day 1, say at 12 noon.
Next day on the return journey, they don't start at the same time. Compared with the previous day, one leaves 36 min earlier (36 mins before 12 noon) and the other leaves 24 mins late (at 12:24)
No, it is not an OG question though the concept tested is very much within the scope of GMAT.
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A bus from city M is traveling to city N at a constant speed while ano 17 Feb 2022, 22:54
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KarishmaB Vinit800HBS

Reading the first half we get:

Let total distance = D
Let Rate of each bus = R

Since they meet at D/2 in 2 hours we can infer that the total time = 4hrs

Now, reading the latter we get

Bus 1 had an early start of 1hr. So for 1hr, the bus drove at a rate of R thereby covering D/4 the distance.

But we see that the extra 1 hour results in the extra 24 miles. So why can't we say that Bus 1 drove at a rate of 24 miles/hour? and hence:

D = R x T
D = 24 x 4 --> 96 miles.
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A bus from city M is traveling to city N at a constant speed while ano 17 Feb 2022, 23:51
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KarishmaB Vinit800HBS

Reading the first half we get:

Let total distance = D
Let Rate of each bus = R

Since they meet at D/2 in 2 hours we can infer that the total time = 4hrs

Now, reading the latter we get

Bus 1 had an early start of 1hr. So for 1hr, the bus drove at a rate of R thereby covering D/4 the distance.

But we see that the extra 1 hour results in the extra 24 miles. So why can't we say that Bus 1 drove at a rate of 24 miles/hour? and hence:

D = R x T
D = 24 x 4 --> 96 miles.
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The highlighted is not correct. 24 miles is the distance of new meeting point from point P ( mid point ). They cover 3D/4 at equal speeds toward each other so each covers 3D/8. This point is D/8 away from mid point so D/8 = 24 miles.

Practice making diagrams to visualise the situation.
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A bus from city M is traveling to city N at a constant speed while ano 18 Feb 2022, 00:06
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Reading the first half we get:

Let total distance = D
Let Rate of each bus = R

Since they meet at D/2 in 2 hours we can infer that the total time = 4hrs

Now, reading the latter we get

Bus 1 had an early start of 1hr. So for 1hr, the bus drove at a rate of R thereby covering D/4 the distance.

But we see that the extra 1 hour results in the extra 24 miles. So why can't we say that Bus 1 drove at a rate of 24 miles/hour? and hence:

D = R x T
D = 24 x 4 --> 96 miles.
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Dear Hoozan,

I am glad that you figured out that the meeting will happen exactly in the middle (Point P). And hence, the deduction that total duration will be 4 hours is perfect.

But, I am afraid that you missed the second aspect.

Read the following again:

Quote:

One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P
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So, the meeting now is taking place at exactly in the middle of the remaining 3/4th Distance.

Check the attachment for the visualization
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Visualization of the situation.png
Visualization of the situation.png [ 99.46 KiB | Viewed 1748 times ]

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A bus from city M is traveling to city N at a constant speed while ano 12 Jan 2025, 11:00
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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.
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As buses travel at constant sam speed, w get Speed = Distance/4. Now on the second day, the first bus starts 1 hr early hence runs D/4 Distance. Hence, the mid point of remaining distance 3D/2 is 24 miles away from original midpoint P (i.e D/2). Hence:
D/2-3D/2= 24
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A bus from city M is traveling to city N at a constant speed while ano 12 Mar 2025, 01:41
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Two buses depart simultaneously from cities M and N and travel towards each other at the same constant speed, heading towards cities N and M, respectively. After two hours of travel, they meet at point P and pass each other to continue towards their destination cities. The next day, both buses are scheduled to simultaneously depart back to their original cities at the same constant speed as the day before. However, one of the buses is delayed by 24 minutes while the other departs 36 minutes earlier than originally scheduled. If they meet 24 miles from point P, what is the distance between cities M and N?

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

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I am assuming the total distance to be 4D. Since both buses travel for 2 hrs each to reach P which is in the middle of MN. Day 1; 🚍 A and 🚌 B has travelled each 2D distances to arrive at point P.

Keep visualising the distance travelled, along with the distance remaining. It’s better to visualise like this —->
DDDD

Day 2, let’s assume 🚌 B starts 36 minutes early. And 🚍 A starts 24 minutes late.

So, the total time gap between buses A🚍 and B 🚌 is 60 minutes (36+24).

In 60 minutes, that’s in 1 hour , bus 🚌 B should have covered D. While bus A hasn’t started yet. Remaining distance 3D.

After one hour, distance covered by buses A and B are D and D respectively.
Total distance bus 🚌 B covered = 2D
And total distance bus 🚍 A covered is D.

Having covered 2D the bus 🚌 B has reached point P.

Now the gap between Bus 🚌 B (which is exactly at point P) and bus 🚍 A is D.

Both buses travel for 30 mins to meet exactly at 24m from point P. 30 mins of travel results in half of the distance. Hence, D/2 = 24. This gives D = 48.

Total distance is 4D = 4*48= 192.

It’s an interesting question. Thanks Bunuel for sharing this question.
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A bus from city M is traveling to city N at a constant speed while ano 12 Mar 2025, 02:53
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Two buses depart simultaneously from cities M and N and travel towards each other at the same constant speed, heading towards cities N and M, respectively. After two hours of travel, they meet at point P and pass each other to continue towards their destination cities. The next day, both buses are scheduled to simultaneously depart back to their original cities at the same constant speed as the day before. However, one of the buses is delayed by 24 minutes while the other departs 36 minutes earlier than originally scheduled.

If they meet 24 miles from point P, what is the distance between cities M and N?

Let the speeds of the buses be x miles per hour

Two buses depart simultaneously from cities M and N and travel towards each other at the same constant speed, heading towards cities N and M, respectively. After two hours of travel, they meet at point P and pass each other to continue towards their destination cities.

Distance MN = 2(x+x) = 4x miles

Point P is at the centre, e.g Distance 2x from M & N each.

The next day, both buses are scheduled to simultaneously depart back to their original cities at the same constant speed as the day before. However, one of the buses is delayed by 24 minutes while the other departs 36 minutes earlier than originally scheduled and they meet 24 miles from point P.

Next day, bus departing from N is delayed by 24 minutes = 24/60 = 2/5 hours while bus departing from M departs 36 minutes = 36/60 = 3/5 hours earlier.

Let us assume that they met t hours after earlier bus departs

Distance travelled by bus departing from N = (t-3/5-2/5)x = x(t-1)
Distance travelled by bus departing from M = xt

xt + x(t-1) = 4x
2xt - x = 4x
t = 5x/2x = 2.5 hours

Distance travelled by bus departing from N = x(t-1) = 1.5x
Distance travelled by bus departing from M = xt = 2.5x

Point P was at 2x, midway between point M& N

Distance from point P = 2.5x - 2x = 2x - 1.5x = .5x = 24 miles; x = 48 miles
MN = 4x = 4*24 = 192 km

IMO E
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