Question

Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Maria drove home, there was no traffic and the trip only took 8 hours. If her average rate was 20 miles per hour faster on the trip home, how far away does Maria live from the mountains?

Answer 1

Maria lives 480 miles away from the mountains.

Step-by-step explanation:

To find the distance between Maria's home and the mountains, we need to determine her average rate or speed. Let's call the distance between her home and the mountains 'd'. We can set up a formula using the average rate formula:

Average rate = distance / time

On the trip to the mountains, it took Maria 12 hours, so her average rate is d/12 miles per hour. On the trip back home, it took her 8 hours and she was driving 20 miles per hour faster, so her average rate is (d/8) + 20 miles per hour. Since the two average rates are equal, we can set up an equation:

d/12 = (d/8) + 20

Multiplying both sides of the equation by 24 (the least common multiple of 12 and 8) to eliminate the fractions, we get:

2d = 3d + 480

480 = d

Therefore, Maria lives 480 miles away from the mountains.