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A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 mph slower than twice the speed of the motorcycle. In two hours, the car is 20 miles ahead of the motorcycle. Find the speed of both the car and the motorcycle, in miles per hour.

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bhuvna789456

The speed of the cycle is 40 miles per hour.

The speed of the car is 50 miles per hour.

Step-by-step explanation:

The given data about the cycle :

Let, the unknown speed of cycle be 'x'.

  • The speed of the cycle (rate) = x mph
  • The time it traveled = 2 hrs
  • The distance covered by cycle in 2 hours = 2x miles

The given data about the car :

The average speed of the car is 30 mph slower than twice the speed of the motorcycle.

  • The speed of the car (rate) = 2x-30 mph
  • The time it traveled = 2 hrs  
  • The distance covered by the car in 2 hours = 2(2x-30) = 4x-60 miles

To find the speed of both the car and the motorcycle :

In two hours, the car is 20 miles ahead of the motorcycle.

Therefore, car distance - cycle distance = 20 miles

(4x-60) - 2x = 20

2x = 20+60

2x = 80

x = 80/2

x = 40 mph

The cycle speed is 40 miles per hour.

The car speed is 2x-30 = 50 miles per hour.

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