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Question

Brian drove to the mountains last weekend. There was heavy traffic on the way there,and the trip took 7 hours.when Brian drove home, there was no traffic and the trip only took 5 hours. If his average rate was 18 miles per hour faster on the trip home, how far away does Brian live from the mountains?

Answer 1

Let's denote the distance Brian lives from the mountains as "d" miles.

On the trip to the mountains, which took 7 hours, Brian's average speed was "d/7" miles per hour.

On the trip back home, which took 5 hours and was 18 miles per hour faster on average, Brian's average speed was "(d/5) + 18" miles per hour.

Since distance = speed x time, we can set up the following equation based on the given information:

Distance to mountains = Distance back home

d = (d/5 + 18) x 5

Simplifying the equation, we get:

d = d + 90

Subtracting "d" from both sides of the equation, we get:

0 = 90

This is not possible, which means there is no valid solution to this problem. Please check the given information and make sure it is accurate.

Answer 2

7 hours in heavy traffic

5 hours in no traffic

18 mph faster with no traffic

distance = time times speed

d = rt

distance is the same either way

f = 18+s

5f = 7s = 5(18+s)

= 90 +5s

2s =90

s= 45 mph

f = 63 mph

63(5) = 315 miles

7(45) = 315 miles