A Tangled Tale

by

Angie Head, Beth Richichi, and Teisha Wright

Problem from Lewis Carroll:

A man walked for 5 hours, first along a level road, then up a hill, and then he turned around and walked back to the starting point along the same path. He walks 4 mph on the level, 3 mph uphill, and 6 mph downhill. Find the distance he walked.

Solution:

Let D(1) be the distance that he walked on level ground, D(2) be the distance uphill, and D(3) be the distance downhill. So D(1) = 4 mph, D(2) = 3 mph, and D(3) = 6 mph. We know that

We also know that D(2) = D(3) since you travel the same distance uphill as you do downhill when you begin and end in the same place. So now, we have


or
.

When we clear the fractions, we get


or

since D(2) = D(3). So, he walked 20 miles in five hours.

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