Maya drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 8 hours. when Maya drove home, there was no traffic and the trip only took 5 hours. if her average rate was 21 miles per hour faster on the trip home, how far away does maya live from the mountains? do not do any rounding.

The distance from her house to the mountains is 280 miles.

Step-by-step explanation:

Let x represent the her speed while driving to the mountains.

if her average rate was 21 miles per hour faster on the trip home, it means that her speed while driving home is (x + 21) mph.

Distance = speed × time

Her trip to the mountains took 8 hours. It means that the distance she travelled on her way to the mountains is 8 × x = 8x

when Maya drove home, there was no traffic and the trip only took 5 hours. It means that the distance she travelled on her way to home is

5(x + 21)

Since the distance is the same, it means that

8x = 5(x + 21)

8x = 5x = 105

8x - 5x = 105

3x = 105

x = 105/3

x = 35 mph

The distance from her house to the mountains is

8 × 35 = 280 miles