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

Answer:

Her average speed is 48 miles per hour.

Step-by-step explanation:

We solve this question using a system of equations.

The speed equation is:

$s = \frac{d}{t}$

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

$s = \frac{320}{t}$

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.

$s - 6 = \frac{280}{t}$

From the first equation:

$s = \frac{320}{t}$

$st = 320$

$t = \frac{320}{s}$

Replacing:

$s - 6 = \frac{280}{t}$

$s - 6 = \frac{280}{\frac{320}{s}}$

$320(s - 6) = 280s$

$320s - 1920 = 280s$

$40s = 1920$

$s = \frac{1920}{40}$

$s = 48$

Her average speed is 48 miles per hour.