Speed, Time and Distance - Quant/Math - CAT 2009

CAT Sample Questions - Question 4 the day : April 7, 2004

The question for the day is on relative speed from the topic Speed, Time and Distance.

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)	400 meters

Explanatory Answer

Note

When a train overtakes another object such as a motorbike, whose length is negligible compared to the length of the train, then the distance traveled by the train while overtaking the motorbike is the same as the length 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

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 given 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 = 5/18 m/sec

Therefore, 36 kmph = 36 * 5 /18 = 10 m/sec.

Relative speed = 10 m/sec. Time taken = 40 seconds.

Therefore, distance traveled = 10 * 40 = 400 meters.