SOLUTION: A family drove to the Grand Canyon, averaging 38 mph. They returned using the same route, averaging 57 mph. If they spent a total of 5 hours driving, how far is their home from the

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Question 1130936: A family drove to the Grand Canyon, averaging 38 mph. They returned using the same route, averaging 57 mph. If they spent a total of 5 hours driving, how far is their home from the Grand Canyon?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Distance each way, d
              SPEEDS      TIME     DISTANCE
TO             38         d/38      d
FROM           57         d/57      d
TOTAL                      5


highlight_green%28d%2F38%2Bd%2F57=5%29

57d%2B38d=5%2A57%2A38

95d=5%2A38%2A57

5%2A19d=5%2A19%2A2%2A57

highlight%28d=114%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


If you note that the ratio of the two speeds is 2:3, then finding the answer is easy with a bit of mental arithmetic.

Since the ratio of 38mph to 57mph is 2:3, the ratio of times at the two speeds (since the distances are the same) has to be 3:2. Since the total time was 5 hours, they spent 3 hours driving there at 38mph and 2 hours driving back home at 57mph.

So the distance from their home to the Grand Canyon is 38*3 = 144 miles, or 57*2 = 114 miles.