Henry Ernest Dudeney/Modern Puzzles/36 - More Bicycling

by : $36$

 * More Bicycling
 * Referring to the last puzzle, let us now consider the case where a third rider has to share the same bicycle.


 * As a matter of fact, I understand that Anderson and Brown have taken a man named Carter into partnership, and the position today is this:


 * Anderson, Brown and Carter walk respectively $4$, $5$ and $3$ miles per hour,
 * and ride respectively $10$, $8$ and $12$ miles per hour.


 * How are they to use that single bicycle so that all shall complete the $20$ miles journey at the same time?