You have decided to take your morning run in preparation for the local marathon at an average speed of 6 miles per hour. Unfortunately you are not in as good a shape as you thought and you are running uphill. You find that complete half of the run, all uphill, at an average of only 3 miles per hour. How fast must your run to make the trip, all downhill, at an average speed for the entire round trip of 6 miles per hour?

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Sorry, you can't do it.
Example: If your run is 6 miles, you would have to do it in 1 hour to achieve the average of 6 miles per hour. As you only started out going 3 miles per hour and have completed half the course, you have taken up that hour and have no time left to go any faster.