Henry Ernest Dudeney/Modern Puzzles/36 - More Bicycling

Modern Puzzles by Henry Ernest Dudeney: $36$

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?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $36$. -- More Bicycling
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $64$. More Bicycling