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Sarah walks uphill at an average of 2 miles per hour, and downhill at an average of 4 miles per hour.
She goes for a 6 mile hike up a hill, and then returns downhill by the same route.

What is Sarah's average speed in miles per hour for the whole journey?
 
 
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.