SOLUTION: A man goes to a place at the rate of 4 kmph. He comes back on a bicycle at 16kmph. His average speed for the entire journey is how much ?

Question 478122: A man goes to a place at the rate of 4 kmph. He comes back on a bicycle at 16kmph. His average speed for the entire journey is how much ?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A man goes to a place at the rate of 4 kmph. He comes back on a bicycle at 16kmph. His average speed for the entire journey is how much ?
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It's similar to parallel resistors or pipes filling tanks, but times 2
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Avg = 2*product/sum
= 2*4*16/(4 + 16) = 128/20
= 6.4 km/hr
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It's always less than the average of the 2 speeds, 4 & 16 --> (10), because more time is spent at the lower speed.
Also notice that the distance is irrelevant.
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I'll work it out:
r1 = rate going, r2 = rate returning, d = distance one-way
t = d/r1 + d/r2 = d(r1 + r2)/r1*r2
t/d = (r1 + r2)/r1*r2
d/t = r1*r2/(r1 + r2)
Avg speed = 2d/t for the round trip
Avg speed = 2*r1*r2/(r1 + r2)

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