Question

Gabriella drives her car 320 miles and averages a certain speed. If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time. What is her average speed?

Answer 1

Her average speed is 48 miles per hour.

Explanation:

We solve this question using a system of equations.

The speed equation is:

`s = (d)/(t)`

In which s is the speed, d is the distance, and t is the time.

Gabriella drives her car 320 miles and averages a certain speed.

So
`d = 320`

Then

`s = (320)/(t)`

If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time.

So, which s - 6, d = 280.

`s - 6 = (280)/(t)`

From the first equation:

`s = (320)/(t)`

`st = 320`

`t = (320)/(s)`

Replacing:

`s - 6 = (280)/(t)`

`s - 6 = (280)/((320)/(s))`

`320(s - 6) = 280s`

`320s - 1920 = 280s`

`40s = 1920`

`s = (1920)/(40)`

`s = 48`

Her average speed is 48 miles per hour.