Raina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Raina drove home, there was no traffic and the trip only took 4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Raina live from the mountains

Question

Mathematics

Skyler Stuart

8 July, 06:11

Raina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Raina drove home, there was no traffic and the trip only took 4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Raina live from the mountains

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Answers (1)

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Desmond Ochoa · Answer 1

Answer: Raina's distance from the mountains is 176 miles

Step-by-step explanation:

Let x represent her average rate on the trip to the mountains.

If her average rate was 22 miles per hour faster on the trip home, it means that her average rate on the trip home is (x + 22) mph

Distance = speed * time

There was heavy traffic on the way there, and the trip took 6 hours. This means that the distance on her way to the mountain is 6x

When Raina drove home, there was no traffic and the trip only took 4 hours. This means that the distance on her way to home is

4 (x + 22)

Since the distance covered is the same, then

6x = 4 (x + 22) = 4x + 88

6x - 4x = 88

2x = 88

x = 88/2

x = 44

Raina's distance from the mountains is

6 * 44 = 176 miles