1.

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(1/2) hours?

Answer»

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.


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