How much time will an express train of length 150 meters and running

Question

How much time will an express train of length 150 meters and running at a speed of 75 kmph take to cross a man walking at 5 m/s inside a passenger train of length 200 meters and running at 15 kmph in a direction opposite to that of the express train. The man is walking inside the train and in opposite direction to that of the train. (Assume the man does not reach the end of his train meanwhile.)

A. 5 sec
B. 6 sec
C. 7.5 sec
D. 8 sec
E. 10 sec

A. 5 sec 
B. 6 sec 
C. 7.5 sec 
D. 8 sec 
E. 10 sec

NoMercy · Accepted Answer

ishant5243 
It's a very simple question if you ignore the length of the passenger train altogether. Just assume that there is an express train running at 75 km/hr and you need to calculate the time it needs to overtake a person walking/running in the same direction on road at speed of 3km/hr( speed of the person in train(18km/hr) - speed of passenger train in opposite direction(15km/hr)).

So now all you need is to divide the length of the express train(150 m) with the relative speed of the express train and person - 72km/hr.

(150*60*60)/72*1000 = 7.5 sec

Please help with Kudos if it helps.

TestPrepUnlimited · Answer

The speed of the express train is the opposite of that of the passenger train and the man walking inside the passenger train.

Therefore the other two speeds are working against the express train.

We can add all the speeds together and treat the entire system as one object. Hence treating the man and passenger train as stationary, the express train has a speed of:

75 km/h + 15 km/h + 5 m/s = 90 km/h + 5 m/s = 90 * 5/18 m/s + 5 m/s = 30 m/s.

The total distance we need to travel however is only 150 meters since the express train is only 150 meters long (or think of it as the time needed for the man to pass the 150-meter express train). Therefore 150 m / (30 m/s) = 5s is the answer.

Ans: A

Stonely · Answer

So according to the question the man is walking from the front of the passenger train to the back so 75 km/h + 15 km/h - 5 m/s = 90 km/h + 5 m/s = 90 * 5/18 m/s - 5 m/s = 20 m/s. that means that 150/20=7.5 and answer C also 5M/sec isn't exactly walking

ishant5243 · Answer

@Bunuel; can you please help with the solution to this problem.

kungfury42 · Answer

It would be helpful to first analyze the man from the ground frame of reference.

The man is inside a train that is moving towards left with a speed of 15kmph or 25/6 mps and the man himself is moving towards right with a speed of 5 mps.

Therefore, from a ground reference, the man is actually moving rightwards with a speed of 5 - 25/6 = 5/6 mps

Now we bring in the express train which is moving rightwards with a speed of 75 kmph or 125/6 mps.

In the frame of reference of this express train, the man is stationary and the train is moving in rightwards direction with a speed of 125/6 - 5/6 = 20 mps

In order to cross the man, the train must cover a distance equivalent to its own length. This with a speed of 20 mps and a length of 150m, the train would take 150/20 = 7.5s to cross the man.

Hence, option C.

Posted from my mobile device

GulfTube · Answer

similar question: https://gmatclub.com/forum/a-train-trav ... 15070.html though this time man is not stationary.

first calculate the net speed of man relative to passenger train:
passenger train: 15km/h = 25/6 m/s
man: opposite direction to passenger train at 5 m/s
their relative speed: 5-25/6 = 5/6 m/s in direction of man's movement.

express train: 75km/h = 125/6 m/s moves same direction to man.
speed of express train relative to man: 125/6 - 5/6 = 20 m/s
to cross the man, express train has to travel it's length of 150m (assuming man's width is negligible) hence the gap distance is of 150m
time it will take for that: 150/20 = 7.5 seconds

How much time will an express train of length 150 meters and running

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How much time will an express train of length 150 meters and running

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