# A car and a bike travelling to cover a distance of 120 km. A car takes 1 hour less than bike to cover the same distance. The average speed of bike is

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A car and a bike travelling to cover a distance of 120 km. A car takes 1 hour less than bike to cover the same distance. The average speed of bike is 10 km/hr less than that of the car. Find the average speed of car and of bike.
1. 20, 50
2. 50, 20
3. 40, 30
4. 30, 40

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Correct Answer - Option 3 : 40, 30

Given

Distance = 120 km

Average speed of car is 10 km more than the speed of bike.

A car takes 1 hour less than bike to cover the same distance.

Formula Used

Time = Distance/ Speed

Calculation

Let the speed of the bike be x km/hr

Then, the speed of the car be (x + 10) km/hr

According to question,

120/x – 120/(x + 10) = 1

⇒ [120(x + 10) – 120 x]/x(x + 10) = 1

⇒ 120x + 1200 – 120x = x2 + 10x

⇒ x2 + 10x – 1200 = 0

⇒ x2 + 40x – 30x – 1200 = 0

⇒ x (x + 40) – 30(x + 40) = 0

⇒ (x – 30) (x + 40) = 0

⇒ x - 30 = 0 or x + 40 = 0

⇒ x = 30 or x = - 40, which is not possible as speed is not negative.

So, bike’s speed = x = 30km/hr.

And car’s speed = x + 10 = 30 + 10 = 40 km/hr.

∴ The average speed of car is 40 km/hr and of bike is 30 km/hr.