quantskillsgmat wrote:A and B starts moving towards each other from newyork and chicago along a straight line with constant speeds.After meeting in midway A reaches chicago in 9 hrs and B newyork in 16 hrs.fied ratio of their speeds.
4:3
3:4
5:4
4:5
1:2

We can plug in the answers, which represent the ratio of A's rate to B's rate.

After A and B meet, A takes less time to finish traveling than B, so A is moving at a faster rate.
Eliminate B, D and E.

Answer choice A: 4:3.
Let A's rate = 4 miles per hour and B's rate = 3 miles per hour.
When elements travel toward each other, we combine their rates, since the elements are working together to cover the distance between them.
Combined rate for A and B = 4+3 = 7 miles per hour.

Let d = 84 miles (the LCM of 4, 3 and 7).
Time for A and B to meet = d/(combined rate) = 84/7 = 12 hours.

In 12 hours, distance traveled by A = r*t = 4*12 = 48 miles.
Remaining distance for A = 84-48 = 36 miles.
Time for A to finish traveling = d/r = 36/4 = 9 hours.

In 12 hours, distance traveled by B = r*t = 3*12 = 36 miles.
Remaining distance for B = 84-36 = 48 miles.
Time for B to finish traveling = d/r = 48/3 = 16 hours.
Success!

The correct answer is A.

this is nice approach but i want some mathemtical approach nt plug in.
can anyone help me.

My approach is as under,

Let d be the distance between New York and Chicago.

Since, A and B meet midway, the distance travelled when they met each other is d/2.

=> A covers the rest of the distance in 9 hrs => d/2 = 9a
and
B covers the rest of the distance in 16 hrs => d/2 = 16b

Eliminating d, we get a/b = 16/9.

I certainly know that this wrong but can you help me with what am I missing in the approach above?

Anurag@Gurome wrote:

bubbliiiiiiii wrote:...Since, A and B meet midway, the distance travelled when they met each other is d/2.

You're not missing anything!
You're assuming extra!

Thanks for clarifying. On self analysis, I reached the same conclusion but just wanted to confirm from a SME.