A is cycling from delhi to mumbai and B from mombai to

Question

A is cycling from delhi to mumbai and B from mombai to delhi(same route). they pass each other and then completed the journeys in 16 and 9 hours respectively. What is the ratio of there speeds.

amips2000 · Answer

I think the answer is 3/4 (ratio of the speeds of A and B).

kpadma · Answer

Does this mean they took 16 and 9 houes to reach from starting
and ennding points, or they took 16 and 9 hours after meeting somewhere
in between?

If it is the later case, I think , the approach should be different.

gmatblast · Answer

This is the correct answer.

Please explain your logic.

Thanks

pakoo · Answer

Agree with kpadma

if the total time is9 and 16 hrs then the answer is 3/4.

but the questions states the time after they meet, in that case howcan the answer be 3/4.

amips2000 · Answer

Hi Gmatblast,
 Here is the way I solved it.

B(ombay)..............M(eeting Point)..............................................D(elhi)


Let X with average speed of 'a' start from B and Y with average speed of 'b' start from D and meet at M.
Since both X and Y started simultaneously from B and D, they take the same time to travel the distance BM and MD respectively.
So, BM/a = DM/b ..........(1a)
 BM/DM = a/b ..........(1)

Now X travels MD in 16 hours and Y travels MB in 9 hours.
So, MD/a = 16 ..............(2a)
 MB/b = 9 ..............(2b)

Hence, BM/MD = (9/16)(b/a) ............(2)

From (1) and (2),

(a/b)^2 = (9/16)

or, (a/b) = (3/4)


I hope this helps.

kpadma · Answer

Nice explanation! thanks!!

vivek_dj · Answer

Rakesh How did u get 9/16..I got the same.

Just used 
Dist=Rate* Time

and since Dist is the same equated both the equations.

Vivek.

rakesh1239 · Answer

I think the question has to be modified. I thought the different way and Vivek I think we were sailing in the same boat for this question.

mdfrahim · Answer

My sincere apologies for not being absolutely clear with the question.
The correct answer is 3:4.
They took 16 and 9 hrs. to reach the destination,after they meet!!!!!!!

A is cycling from delhi to mumbai and B from mombai to

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