# GMAT Math Practice - Speed Time Races

Concept: Computing distance travelled. Converting from one units to another.

A GMAT Math practice question in speed, distance, and time. Concept: Finding length of train when it crosses another moving object.

#### Question: 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

Video explanation will be added soon
##### Concept : 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
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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