Amotor scooter travels 18 mi in the same time that a bicycle covers 8 mi. if the rate of the scooter is 5 mph more than twice the rate of the bicycle, find both rates.

If you would like to find the rate of the bicycle and the scooter, you can do this using the following steps:

a scooter: 18 miles ... 2 * r + 5 mph
a bicycle: 8 miles ... r = ? 

18 * r = 8 * (2 * r + 5)
18 * r = 16 * r + 40
18 * r - 16 * r = 40
2 * r = 40
r = 20 mph

a bicycle: r = 20 mph
a scooter: 2 * r + 5 mph = 2 * 20 + 5 = 45 mph

The correct result would be: The rate of the scooter is 45 mph and the rate of the bicycle is 20 mph.