February 2014
Problem of the Month

Hobo Problem
by Sam Lloyd

Weary Willie, a hobo who had outstayed his welcome at Joytown, started for Pleasantville at the same time that Dusty Rhodes started his trip from Pleasantville to Joytown.   They met and exchanged the fraternal grip at a point where Willie had gone 18 miles farther than Dusty.   After an affectionate parting, it took Willie 13.5 hours to reach Pleasantville, and Dusty 24 hours to get to Joytown.   Assuming that each hobo traveled at a constant rate, how far was it from Pleasantville to Joytown?

Please send in your original equation that you needed to solve this problem.

Solution to the Problem:

The answer is 126 miles from Pleasantville to Joytown.

Let x = the distance that Dusty had traveled when he met up with Willie.   Then x + 18 represents the distance that Willie had traveled.   So, the total distance between pleasantville and Joytown is 2x + 18.

Now look at the diagram below and set up a Rate-Times-Distance box to determine the rates of each traveler, since we know their distances and times:


Now use these rates to set up an equation using the distances that each traveled in the same time period (when they met):




So, x = 54 miles which represents the distance Dusty had traveled when he met Willie.
Then, x + 18 = 72 miles, the distance that Willie had traveled.
Therefore the distance between Pleasantville and Joytown is 54 + 72 = 126 miles.

Correctly solved by:

1. James Alarie

Flint, Michigan

Send any comments or questions to: David Pleacher