Acar travels 237 miles in the same time that a motorcycle travels 207 miles. if the car's speed is 10 miles per hour more than the motorcycle's, find the speed of the car and the speed of the motorcycle.

Speed of motorcycle = x

speed of car = X +10

travel time = distance / speed

car travel time = 237 /(x+10)

motorcycle travel time = 207/x

set them to equal each other:

237/x+10 = 207/x

cross multiply:

237x = 207(x+10)

distribute the right side:

237x = 207x + 2070

subtract 207x from both sides:

30x = 2070

divide both sides by 30:

x = 2070 / 30
x = 69

speed of motorcycle was 69 miles per hour
speed of car was 69 +10 = 79 miles per hour