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

In your image, you mention that "case 2" both cover 1.5d distance each till P' But wouldn't one bus cover 2.5d and the other 1.5d?

Hi Hoozan,

Each will cover 1.5d distance AFTER M has already traveled for initial 1 hour.
You are right about the part that M will cover 2.5d and N will cover 1.5d.

But as you can see, I have placed M not at the starting point but at a certain distance ‘D’ from its initial starting point.

Posted from my mobile device

Ahh! Got it. Thanks a lot

Solution
• Time taken by buses to complete dist. Between M & N: 4 hr.
• Let, the const. speed of both the buses be x miles/hr.
• The total length of the journey: is 4x miles.
• Meeting point P: 2x, reason: both buses have the same speed, so they will meet at the midpoint.
• During the return journey, one bus starts 36 min early -> 0.6 hr & the other bus starts 24 min late -> 0.4 hr. From these two statements: one bus covers dist : x*(0.6+0.4) -> x. Before the other bus starts heading back.
• So remaining dist that both will travel is: 4x-x = 3x.
• The meeting point will be half of this 3x miles dist. -> 1.5x
• We know that they meet 24 miles from point P,
that implies:
-> 2x-1.5x = 24;
-> 0.5x=24
-> x=48
• The required dist is 4x. Therefore, 4x= 192 miles (dist between two cities)

Think of this question in terms of a straight line divided in 4 parts as follows

M------------X------------P------------Y------------N

Both buses meet halfway at P because they are travelling at the same speed.
Next day, one bus leave one hour before the other bus (24+36)
Let's assume that bus that left 1 hour early left from M.
In 1 hour, the bus would've travelled 1/4th of the total distance and would be at point X.
Now, the bus at N starts its journey and the two buses meet halfway of the remaining 3/4th of the distance say at point R.
Point R would be half of 3/4th = 3/8
Now we are given that the distance between P and the return trip's meeting point (R) is 24

So, P - R = 24
P = x/2
R = 3x/8

x/2 - 3x/8 = 24
x/8 = 24
x = 192

Let the total distance be d.

As the speed of both buses is constant, they meet halfway through at d/2.

Speed of both the buses together = 1/2 => speed of each bus = (1/2)/2 = 1/4

On the second day, assume the bus (b2) from M starts 1 hour earlier, hence covers 1/4d in 1 hour. Remaining distance = 3d/4

Distance traveled by each bus (3d/4)/2 = 3d/8

Now the total distance d = 3d/8 + d/2 + 24 (you can infer this when you visualize a diagram) => 1d/8 = 24 => d = 192 [E]

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.