Question

ii) If the speed of a car is decreased by 8 km/h, it takes 1 hour more to cover a
distance of 240 km. Find the original speed of the car.
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Answer 1

Answer:

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Answer 2

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

Step-by-step explanation: