GMAT Quant Questions | GMAT Rates Q2

Length of Train | Relative Speed | Speed Distance Time | GMAT Sample Questions

This sample GMAT Math question is a Rates, Time & Distance Problem solving question. The concept tested is to find the length of a train applying the concept of relative speed of two objects travelling in the same direction. A medium difficulty, GMAT 650 level sample question.

Question 2: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?

  1. 1777 meters
  2. 1822 meters
  3. 400 meters
  4. 1111 meters
  5. None of these

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Explanatory Answer | GMAT Time Speed Distance

Distance covered by train when it crosses a moving object

When a train overtakes another object such as a motorbike, whose length is insignificant compared to the length of the train, the distance traveled by the train is equal to the length of the train.

Because the motorbike is also moving, we have to take the relative speed between the train and the motorbike and not just the speed of the train.

The length of the train = distance traveled by the train while overtaking the motorbike
= relative speed between the train and the motorbike × time taken to overtake the motorbike

In this case, as both the objects i.e., the train and the motorbike are moving in the same direction, the relative speed between them = difference between their respective speeds
= 100 - 64 = 36 kmph.
Distance traveled by the train while overtaking the motorbike = 36 kmph × 40 seconds.

The final answer is in meters and the speed is given in kmph and the time in seconds.
So let us convert the given speed from kmph to m/sec.

1 kmph = \\frac{5}{18}) m/sec
Therefore, 36 kmph = 36 × \\frac{5}{18}) = 10 m/sec.
Relative speed = 10 m/sec.
Time taken = 40 seconds.
Therefore, distance traveled = 10 × 40 = 400 meters.

Choice C is the correct answer.

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