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Algebra Level 3

Jon drives from his home to the store at an average speed of 40 40 kilometers per hour. He drives back home from the store at an average speed of 60 60 kilometers per hour. Assume the distance he travels in these two trips is the same. His average speed for the entire trip is how many kilometers per hour?

46 52 50 48

Steven Yuan by Steven Yuan , 20, USA

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2 solutions

Let x be the distance. So time for forward drive is x/40 hr. For back it is x/60.
A v e r a g e s p e e d = t o t a l d i s t a n c e t o t a l t i m e = 2 x x 40 + x 60 = 48 48 Average~~ speed = \dfrac{ total ~distance}{total~ time} \\= \dfrac{2x}{ \dfrac{x}{40} + \dfrac{x}{60} } = 48\\ \boxed{48}

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Fox To-ong
Feb 8, 2015

by FOX'S THEOREM, AVERAGE VELOCITY IS THE SAME AS THE HARMONIC MEAN = 2ab/a+b

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