Question

Prabhat cycled a distance of 240 kilometers at a certain speed. if he cycled 3km faster, he would have taken 4 hours fewer to reach the distance. what was the speed in km/h at which Prabhat actually cycled?

1. 12 km/hr
2. 10 km/hr
3. 8 km/hr
4. 14 km/hr

Answer 1

Correct Answer - Option 1 : 12 km/hr

Given :

Distance = 240 km

Formula Used:

Time = Distance ÷ Speed

Calculations:

Let the speed be x km/h

If he cycled 3km faster every hour, the speed will be (x + 3) km/h

Time needed when the speed is x km/h = 240/x hour

Time needed when the speed is (x + 3) km/h = 240/(x + 3) hour

According to Question,

The difference in time taken is 4 hours

240/x - 240/(x + 3) = 4

⇒ 240(x + 3) - 240x = 4x(x + 3)

⇒ 240x + 720 - 240x = 4x² + 12x

⇒ 4x² + 12x - 720 = 0

⇒ x² + 3x - 180 = 0

⇒ (x - 12)(x + 15) = 0

⇒ x = 12 or x = -15 (rejected, since speed cannot be negative)

⇒ Speed = x = 12 km/h

∴ Prabhat is cycling at 12 km/h