Henry Ernest Dudeney/Puzzles and Curious Problems/138 - The Three Workmen/Solution

by : $138$

 * The Three Workmen

Solution
Alfred, Bill and Casey would take respectively $14 \tfrac {34} {49}$ days, $17 \tfrac {23} {41}$ days, and $23 \tfrac 7 {31}$ days.

Proof
Let $a, b, c$ be the rate of working in jobs per day of (respectively) Alec, Bill and Casey.

Let $t_a, t_b, t_c$ be the number of days it would take (respectively) Alec, Bill and Casey to do the job alone.

We have:

and so:

Hence and so.

Also see

 * Henry Ernest Dudeney: Modern Puzzles: $84$ - The Three Brothers, exactly the same problem but with different names.