#### Question

A car with speed 60 km/hr takes 8 hours to travel some distance. What should be the increase in the speed if the same distance is to be covered in 7\[\frac{1}{2}\] hours?

#### Solution

The speed of the car is inversely proportional to the time taken by the car to travel the distance.

Let the speed of the car be s and the time taken by the car to travel the distance be t.

Here, s varies inversely as t i.e. \[s \propto \frac{1}{t}\] .

∴ \[s = \frac{k}{t}\] , where is k is constant of variation

⇒ s × t = k

When s = 60, t = 8.

∴ k = 60 × 8 = 480

So, the equation of variation is st = 480.

When t = \[7\frac{1}{2}\] h = \[\frac{15}{2}\] h,

\[s \times \frac{15}{2} = 480\]

⇒ \[s = \frac{480 \times 2}{15}\] = 64 km/h

∴ Increase in the speed = 64 − 60 = 4 km/h

Thus, the increase in the speed of the car is 4 km/h.