Let v represent the speed of car in km/hr and t represent the time required. Since, speed of a car varies inversely as the time required to cover a distance.
∴ v ∝ (1/t)
∴ v = k x (1/t)
where, k is the constant of variation.
∴ v × t = k …(i)
Since, a car with speed 60 km/hr takes 8 hours to travel some distance. i.e., when v = 60, t = 8
∴ Substituting v = 60 and t = 8 in (i), we get
v × t = k
∴ 60 × 8 = t
∴ k = 480
Substituting k = 480 in (i), we get
v × t = k
∴ v × t = 480 …(ii)
This is the equation of variation.
Now, we have to find speed of car if the same distance is to be covered in 7(1/2) hours. i.e., when t = 7(1/2) = 7.5, v =?
∴ Substituting, t = 7.5 in (ii), we get
v × t = 480
∴ v × 7.5 = 480
v = 480/7.5 = 4800/75
∴ v = 64
The speed of vehicle should be 64 km/hr to cover the same distance in 7.5 hours.
∴ The increase in speed = 64 – 60 = 4km/hr
∴ The increase in speed of the car is 4 km/hr.
