Question

Mary drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Mary drove home, there was no traffic and the trip only took 4 hours. If her average rate was 27 miles per hour faster on the trip home, how far away does Mary live from the mountains? Do not do any rounding.

Answer 1

There are two separate equations for this question that use the same variable.

Mary took 7 hours to complete a trip with traffic. This would use the following expression:

$7x$

Mary took 4 hours to complete the same trip without traffic. The average rate of speed was 27 mph faster than the trip with traffic. This uses the following expression:

$4(x+27)$

Both trips had the same distance. From the information provided, we can set up the following equation:

$7x = 4(x+27)$

x represents the average rate of speed on both trips.

Distribute 4 to each term in parentheses:

$4 \times x = 4x$
$4 \times 27 = 108$

$7x = 4x + 108$

Subtract 4x from both sides:

$3x = 108$

Divide both sides by 3 to get x by itself:

$x = 36$

The average speed for the slower trip is 36 mph.

We can plug this value into the first equation:

$7(36) = 7 \times 36 = 252$

Mary lives 252 miles away from the mountains.