George runs up hill 6 miles per hour and downhill at 12 miles per hour. On the flat he runs at 9 miles per hour. He runs to inspiration point: an easy route, as it is all on the flat apart from heartbreak hill, on which he runs up one side and down the other. upon arriving at inspiration point george immediately turns around and runs back along exactly the same route. the round trip takes 45 minutes. How far away is inspiration point?
Answers
Given : George runs up hill 6 miles per hour and downhill at 12 miles per hour. On the flat he runs at 8 miles per hour.
He runs to inspiration point: an easy route, as it is all on the flat apart from heartbreak hill, on which he runs up one side and down the other. upon arriving at inspiration point george immediately turns around and runs back along exactly the same route. the round trip takes 45 minutes.
To Find : How far away is inspiration point?
Solution:
correction in Question : (On the flat he runs at 8 miles per hour)
Let say Distance up hill = D
Time taken for uphill = D/6
Time taken to down hill = D/12
Total time taken = D/6 + D/12 = (2 + 1)D/12 = 3D/12 = D/4
Total Distance = D + D = 2D
Hence average speed for uphill and down hill for equal distance = 2D/(D/4)
= 8 miles per hr
So Average speed = 8 miles per hr
round trip takes 45 minutes. => total Distance = 8 * 45 / 60
= 6 miles
One side distance = 6/2 = 3 miles
inspiration point is 3 miles away
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