Problem Solving

AAPL wrote:e-GMAT

A car overtakes a goods train, which is 400 m long and running at 36 kph, in 8 secs. The same car crosses another goods train, which is running from opposite direction at 54 kph, in 4 secs. How long the faster train will take to cross the slower train?

A. 28 seconds
B. 2 minutes
C. 2 minutes 20 seconds
D. 3 minutes 20 seconds
E. 3 minutes 40 seconds

OA A.

We must assume that the length of the car is negligible.

Say the speed of the car is x kmph.

Since it is given that the car overtakes the first goods train, the relative speed of the car = x - 36

Time taken to overtake the goods train = (400/1000) / (x - 36) = 8/3600

x = 216 kmph

Again, since the other goods train is moving in the opposite direction, the relative speed = x + 54 = 216 + 54 = 270 kmph

Say the length of the other goods train is L meters

Time taken to overtake the second goods train = (L/1000) / 270 hours = [(L/1000) / 270]*3600 seconds = 4 seconds

=> L = 300 meters

Now since the slower train and the faster train are moving in the opposite direction, their relative speed = 36 + 54 = 90 kmph

Time taken to by the faster train to overtake the second goods train = {(400 + 300)/1000} / 90 hours = 28 seconds.

The correct answer: A

Hope this helps!

-Jay
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