A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is \( 30 \mathrm{mph} \) 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.
Car Speed:
Motorcycle Speed:

Answer

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Answer

Car's distance - Motorcycle's distance = 20, so (2x - 30)(2) - (2x)(2) = 20

Steps

Step 1 ：Let x = speed of motorcycle in mph, then 2x - 30 = speed of car in mph

Step 2 ：Car's distance = (2x - 30)(2), Motorcycle's distance = 2x(2)

Step 3 ：Car's distance - Motorcycle's distance = 20, so (2x - 30)(2) - (2x)(2) = 20