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Sarah takes 3 hours to climb the hill, and $1\frac{1}{2}$ hours to get down.
So altogether her journey takes $4\frac{1}{2}$ hours.

In this time she travels $12$ miles, so her average speed is
$12 \div 4\frac{1}{2} = 12 \times \frac{2}{9} = 2\frac{2}{3}$ miles per hour.


 
 

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This problem is taken from the UKMT Mathematical Challenges.