Henry Ernest Dudeney/Modern Puzzles/16 - Digging a Ditch

Modern Puzzles by Henry Ernest Dudeney: $16$

Digging a Ditch

Here is a curious question that is more perplexing than it looks at first sight.

Abraham, an infirm old man, undertook to dig a ditch for $2$ pounds.

He engaged Benjamin, an able-bodied fellow, to assist him and share the money fairly according to their capacities.

Abraham could dig as fast as Benjamin could shovel out the dirt,

and Benjamin could dig four times as fast as Abraham could do the shovelling.

How should they divide the money?

Of course, we must assume their relative abilities for work to be the same in digging or shovelling.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Money Puzzles: $16$. -- Digging a Ditch
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Money Puzzles: $9$. Digging a Ditch