Question

A motorcycle travels 6 mph faster than a sport car. if the sports car can only go 90 miles in the same time that the motorcycle can go 99 miles, find speed of the motorcycle

the speed of the motorcycle is ...... miles per hour

Answer 1

The speed of the motorcycle is 66 miles per hour.

Explanation:

We use the following relation to build a system of equations.

`v = (d)/(t)`

In which v is the velocity, d is the distance, and t is the time.

Car:

`v_(c) = (d_(c))/(t)`

We have that the car travels 90 miles, so
`d_c = 90`

Then

`v_(c) = (90)/(t)`

`t = (90)/(v_(c))`

a motorcycle travels 6 mph faster than a sport car.

This means that
`v_m = 6 + v_(c)`, so
`v_(c) = v_m - 6`

Travels 99 miles, so
`d_m = 99`

`v_(m) = (99)/(t)`

Since
`t = (90)/(v_(c))` and
`v_(c) = v_m - 6`, we have that
`t = (90)/(v_(m) - 6)`

So

`v_(c) = (99)/(t)`

`v_(m) = (99)/((90)/(v_(m) - 6))`

`v_m = (99(v_(m) - 6))/(90)`

`99(v_(m) - 6) = 90v_m`

`99v_m - 594 = 90v_m`

`9v_m = 594`

`v_m = (594)/(9)`

`v_m = 66`

The speed of the motorcycle is 66 miles per hour.