A Tangled Tale

A 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.


There is not enough information given to solve the problem.

Hint in setting up an equation?


Another Hint?

Carroll's version gave the total time as 6 hours. Polya used the total time of 5 hours. Is your solution appropriate for either version?

Return to the EMAT 4600/6600


Carroll, Lewis (1885) A Tangled Tale. Currently available at http://ebooks.adelaide.edu.au/c/carroll/lewis/tangled

Note: Lewis Carroll (real name, Charles Lutwidge Dodgson) published the ten problems between 1880 and 1885 in The Monthly Packet magazine. They were published in book form in 1885 with illustrations. With each problem (Carroll called them Knots) readers were invited to send solutions and Carroll commented on the solutions he received. This problem was Knot 1 Excelsior phrased in a story about two knights who travel for 6 hours at the rate of 4 mph on level ground, 3 mph going up hill, and 6 mph going down hill. They are late for dinner but curious about how far they traveled.

Polya, George (1962) Mathematical Discovery: On understanding, learning, and teaching problem solving. Volume 1. New York: John Wiley & Sons.

Polya presents his version of the problem in Chapter 2, pp 41- 42. He present two different solutions but uses his explanations to make some points about the solution process.