Henry Ernest Dudeney/Puzzles and Curious Problems/139 - Working Alone/Solution

by : $139$

 * Working Alone

Solution
Alfred would take $60$ days, while Bill would take $40$ days.

Proof
Let $t_a$ and $t_b$ be the time taken for Alfred and Bill to do the job.

Let $a$ and $b$ be the rate in days at which Alfred and Bill can do the job.

In $24$ days, the contributions of Alfred and Bill is $24 a$ and $24 b$ respectively.

So for the total contribution to the job, we have:

We have:

and so:

So Alfred would take $60$ days, while Bill would take $40$ days.