Problem 7

Three men, Atkins, Brown, and Cranby, had to go a journey of forty miles. Atkins could walk one mile an hour, Brown could walk two miles an hour, and Cranby could go in his donkey cart at eight miles an hour. They start at the same time. Cranby drove Atkins a certain distance, and dropping him to walk the remainder, drove back to meet Brown on the way and carried him to their destination, where they all arrived at the same time. How long did the journey take? Of course each went at a uniform rate throughout.

[Problem submitted by Kevin WindsorKevin Windsor, LACC Associate Professor of Mathematics. Source: Henry Ernest Dudeney, 536 Puzzles & Curious Problems, 1967]

Solution for Problem 7:

Let x = distance Atkins (A) rode with Cranby (C) and y = distance Brown (B) walked. Using d/r = t,

Being that they all arrived at the same time,

+ = + à 7x + 3y = 280 and

+ = + + à 2x – 5y = 0. Solving this system gives x = and y = . Substituting in A or B gives the total time for the journey to be 10 hours.