The time taken by a train to cover a fixed distance and the speed of the train is in ____ proportion.

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Detailed Solution

The time taken by a train to cover a fixed distance and the speed of the train is in inverse proportion.
We know that two variables are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y

are two variables in inverse variations, then

x ∝ 1 y ⇒ x = k 1 y ⇒ x = k y,        where k is proportianality constant ⇒ x y = k .... (1)

We know that,

Distance = Speed × Time ⇒ Speed = Distance Time

Let’s assume distance = 50 km in 1 hour.

⇒ Speed = 501

⇒ Speed = 50 km/hr

And also let distance = 50 km for 2 hour.

⇒ Speed = 502

⇒ Speed = 25 km/hr

This shows that speed reduces as time goes on.
Thus, the time taken by the train to cover a fixed distance and the speed of the train is in inverse proportion.

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