# Speed, Time and Distance

Concept: Computing distance travelled. Converting speed, distance from one unit to another.

A GMAT quant practice question in rates - speed, distance, and time. Concept covered: Finding the length of a platform when a train crosses the platform.

#### Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

1. 240 meters
2. 360 meters
3. 420 meters
4. 600 meters
5. Cannot be determined

Video explanation will be added soon
##### Distance covered by the train when crossing a man and when crossing a platform

When a train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.
However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.

The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover. i.e., length of the platform.

##### Compute length of platform

Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 72 kmph * 12 seconds

Convert 72 kmph into m/sec
1 kmph = $$frac{5}{18}\\$ m/s$This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 72 kmph = $\frac{5}{18} * 72\\$ = 20 m/sec

Therefore, length of the platform = 20 m/s * 12 sec = 240 meters.

Choice A is the correct answer.

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