Question

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

Answer 1

Eric lives 252 miles away from the mountains.

Step-by-step explanation:

To find the distance Eric lives from the mountains, we need to determine the average speed he traveled on each leg of the trip. Let's say the distance between Eric's home and the mountains is 'd' miles.

1. We know that the trip to the mountains took 7 hours, so the average speed of this leg can be represented as d/7.
2. The trip back home took 4 hours, and his average speed was 27 miles per hour faster than on the way there. So the average speed on this leg can be represented as d/4 + 27.

Since the average speed is equal to the total distance divided by the total time, we can set up the equation:
d/7 = d/4 + 27

Multiplying both sides of the equation by the least common denominator (28), we get:
4d = 7d + 756

Simplifying the equation:
3d = 756
d = 252

Therefore, Eric lives 252 miles away from the mountains.

Answer 2

Eric drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours.When Eric drove home, there was no traffic and the trip only took 4 hours.If his average rate was 27 miles per hour faster on the trip home, how far away does Eric live from the mountains?
let s = his speed in trafficthen (s+27) = his speed coming homeWrite a distance equation; dist = time * speedthe dist there and back was the same, therefore7s = 4(s+27)7s = 4s + 1087s - 4s = 1084s = 108s = 108/4 s = 27 mph in traffic"how far away does Eric live from the mountains?"7 * 27 = 189 miles