Speed and time vary in ____ proportion to each other while the distance is kept constant.

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Detailed Solution

Speed and time vary in inverse proportion to each other while the distance is kept constant.
It is given that the distance is kept constant.
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)

Therefore, when the product of the values of two quantities is constant, the two quantities vary inversely.
We know that,

Speed = Distance Time ⇒ Speed × Time = Distance

Since it is given that distance is constant, therefore

⇒ Speed × Time = Constant

Since, the product of speed and time is a constant, it follows that speed and time vary inversely.
Therefore, speed and time vary in inverse proportion to each other while the distance is kept constant.

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