SOLUTION: What is the average speed of a cyclist who bikes up a hill at 6mph but then bikes back along the same path down the hill at 12 mph?

Question 803144: What is the average speed of a cyclist who bikes up a hill at 6mph but then bikes back along the same path down the hill at 12 mph?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What is the average speed of a cyclist who bikes up a hill at 6mph but then bikes back along the same path down the hill at 12 mph?
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Avg = 2*6*12/(6+12)
= 8 mi/hr
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d = r*t
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r1 = going
r2 = returning
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t = d/r1 + d/r2 (d = one-way distance)
t = (d*r1 + d*r2)/(r1*r2)
t = d*(r1+r2)/(r1*r2)
For the round-trip:
t = 2d*(r1+r2)/(r1*r2)
r for round trip = 2d/t
t/2d = (r1+r2)/(r1*r2)
Invert
2d/t = r1*r2/(r1+r2)
Using 2d for distance
avg r = 2r1*r2/(r1+r2)
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This is similar to parallel resistances and parallel flows, but with a factor of 2 for the round-trip (of trips of equal distance)
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