If the speed of a car is decreased by 8km per hour, it takes 1 hour more to cover a distance of 240km. Find the original speed of the car
Answers
Answer: 48km/hr
Step-by-step explanation:
Answer:
48 km/h
Step-by-step explanation:
Let the initial speed of the car be x km/h.
If the speed is decrease by 8 km/h the new speed will be :
(x - 8) km/h
Given the distance = 240 km
Time = Distance / speed
The initial time taken = 240/x
The time taken after the speed is decreased = 240/(x - 8)
Now the time it takes to cover the 240 km after the speed is reduced is one hour more than the time taken to cover the same distance using the initial speed.
We substitute this relationship as follows:
240/(x - 8) - 240/x = 1
Solving for x :
x(240) - 240(x - 8) = x(x - 8)
240x - 240x + 1920 = x^2 - 8x
1920 = x^2 - 8x
x^2 - 8x - 1920 = 0
The roots are - 48 and 40
We substitute as follows :
x^2 - 48x + 40x - 1920 = 0
x(x - 48) + 40(x - 48) = 0
(x + 40) (x - 48) = 0
x = - 40 or 48
We take the positive value since speed cannot be negative.
The initial speed of the car is hence :
48 km/h