A car with speed 60 km/hr takes 8 hrs to travel some distance .What should be the increase in the speed if the same distance is to be covers in 7 1/2 hours ?
Answers
Answer:
Let the speed of car in km/hr be = ‘v’
The time required be =‘t’
Since, speed of a car varies inversely as the time required to cover a distance.
v ∝ 1/t
v = k × (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.
When v = 60, t = 8
Substitute the value of v = 60 and t = 8 in (i), we get
v × t = k
60 × 8 = t
k = 480
Now, substitute the value of k = 480 back in (i), we get
v × t = k
∴ v × t = 480 … (ii)
This is the equation of variation.
Now, let us find the speed of car if the same distance is to be covered in 7 ½ hours.
When t = 7 ½ = 7.5, v =?
Substitute the value of t = 7.5 in (ii), we get
v × t = 480
v × 7.5 = 480
v = 480/7.5
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.