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The average speed that cannot be reached

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A driver wants to average 60 mph over a journey. She drives the first half of the distance at 30 mph.

How fast must she drive the second half of the distance to achieve the 60 mph average?

The obvious answer, 90 mph, is wrong. So is every other number.

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Work out how long the whole journey would have to take at a 60 mph average, and how much of that time the first half has already used.

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