# Inverse Variation

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In an inverse variation the change in two variables is such that with an increase in the first variable the second variable decreases. But if the first variable decreases then an increase in the second variable is recorded. The relation of the speed of a vehicle and the time taken by the vehicle to cover a certain distance is an example of inverse variation.

Inverse variation can be represented as xy = k
Where x and y are variables and k is a constant of proportionality.

Example 1: If a biker drives at 50 miles per hour and takes 1.5 hours to cover a certain distance, what will be the constant of proportionality?

Solution: The two variables we have are the speed of the bike s and time taken to cover the distance t. Variable s and t have inverse variation with respect to each other.

Thus the inverse variation is st = k

Putting the values, 50 x 1.5 = k

k = 75

Thus the constant of proportionality is 75.

Example 2: The time taken by an ice cube of one square inch to melt at 78 degrees is 3 hours. Find the constant of
proportionality.

Solution: We have two variables here. The first variable is the time taken (h) to melt. The second variable is the temperature (t)
at which the ice cube is melting.

Thus, ht = k

Putting the values of the variables we get,

3 x 78 = k

k = 234

Thus the constant of proportionality is 234.