Dale drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Dale 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 Dale live from the mountains? Do not do any rounding.

Question

11-11-2017
Mathematics

contestada

Dale drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Dale 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 Dale live from the mountains? Do not do any rounding.

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swaggernaut swaggernaut · Answer 1 · 2017-11-11T04:19:38+01:00

if you let X = the distance in miles from Dales's house, and understand rate = distance/ time, the rate going to mountains = x/7, and back from mountains is x/5. If dale was 18mph fast going home, the equation would be...
(coming home rate) = (going to mountain rate) + 18 which is
x/5 = x/7 + 18. Then solve for X.
Use the least common denominator = 35 so multiply everything by 35 and you get...

7x = 5x+630
simplify...
2x = 630, then
x = 315 .
Dale live 315 miles away from the mountains.