A car and motorcycle take off at the same place. 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. Fine the speed of both in mph.

Let the speed of the motorcycle by x mph. Then the speed of the car is (2x - 30) mph.

In 2 hours the motorcycle drove 2x miles and the car drove 2(2x - 30) miles. The difference between these results is given to be 20 miles.

Hence, 2(2x - 30) - 2x = 20; 4x - 60 - 2x = 20; 2x = 20 + 60 = 80, and x = 40.

Answer: the speed of the motorcycle is 40 mph and the speed of the car is 50 mph.

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