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The easiest wau to solve this is to think of a number that both 5 and 10 go into. Say 10.

Suppose each half of the race was 10 miles long.

Then the first half, at 5 mph, takes 2 hours. The second half, at 10 mph takes one hour. Than makes 3 hours in all to run the 10+10 = 20 miles.

So average speed = 20/3 = 6.67 mph.

The required answer is known as the Harmonic mean of the two speeds.

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Q: If the first half of a race was run at 5 miles per hour and the second half at 10 miles per hour what is the average speed?
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