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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 α 1/t`.
∴ \[s = \frac{k}{t}\] , where 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.
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