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Sarah goes up a hill and then down again the same way. On the way up she averages $2$ miles per hour. On the way down she averages $4$ miles per hour. What is Sarah's average speed in miles per hour for the whole journey? Give an exact answer.
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
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