Two trains A and B are running in opposite directions from stations Q

Question

Two trains A and B are running in opposite directions from stations Q and P towards their destinations P and Q respectively. Train A takes 25 hours and Train B takes 36 hours after crossing each other to reach their destinations, If the speed of train A is 108 miles/hr, then find the speed of the other train?

A. 75
B. 120
C. 84
D. 90
E. 96

Show Answer

Official Answer

D

A. 75
B. 120
C. 84
D. 90
E. 96

Krunaal · Accepted Answer

Whenever two entities starting from opposite ends at the same time meet at a common point and the total distance they travelled is D, the ratio of their speeds \(\frac{Sa}{Sb} = \sqrt{\frac{Tb}{Ta}}\), where Tb and Ta is the time taken to reach their destination from the common point.

\(\frac{108}{Sb} = \sqrt{\frac{36}{25}}\)

\(\frac{108}{Sb} = \frac{6}{5}\)

\(\frac{18}{Sb} = \frac{1}{5}\)

\(Sb = 5*18 = 90\)

Answer D.

\frac{108}{Sb} = \sqrt{\frac{36}{25}}

\frac{108}{Sb} = \frac{6}{5}

\frac{18}{Sb} = \frac{1}{5}

Sb = 5*18 = 90

Answer D.

lewdtoucan · Answer

Helo, thanks for sharing the solution!

Is this tested on GMAT? I found no reference to this formula on TTP. Also, could you please explain how the formula could be derived?

HarshavardhanR · Answer

GMAT-Club-Forum-zyaifqyy.png One way to solve this question. --- Harsha

lewdtoucan · Answer

Thanks for sharing an alternative solution, Harsh!

Question: Why are you assuming that the time taken by train A to cover QM, is equal to the time taken by train B to cover PM? Does the question support this assumption in any way? Thanks in advance!

HarshavardhanR · Answer

Hey!

The point you are raising is legit . I believe that ideally,  the question should have mentioned that the trains start at the same time from their respective stations .

My solution (and the one above, from what I see!) implicitly assumed this. Typically, the question stem will mention this.

So, unless I am missing something here, the question may be a bit incomplete (happy to be corrected!).

Now, if it is considered as true that the two trains started from their respective stations at the same time,

then ->

Point M is where they meet. In other words,  in the same time  that A took to reach M from Q, B reached M from P. Hence, the 2 trains would meet at M.

Hope this helps!

Harsha

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Two trains A and B are running in opposite directions from stations Q

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