Henry Ernest Dudeney/Puzzles and Curious Problems/133 - Sawing and Splitting/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $133$

Two men can saw $5$ cords of wood per day,

or they can split $8$ cords of wood when sawed.

How many cords must they saw in order that they may be occupied for the rest of the day in splitting it?

$3 \tfrac 1 {13}$ cords

Let $n$ be the number of cords they are to work on.

We have that:

$\dfrac n 5 + \dfrac n 8 = 1$

from which we get:

$8 n + 5 n = 40$

That is:

$n = \dfrac {40} {13} = 3 \tfrac 1 {13}$

$\blacksquare$