Henry Ernest Dudeney/Modern Puzzles/15 - Sawing Logs

by : $15$

 * Sawing Logs
 * "Your charge," said Mr. Grigsby, "was $30$ shillings for sawing up $3$ cords of wood made up of logs $3$ feet long,
 * each log to be cut into pieces $1$ foot in length."


 * "That is so," the man replied.


 * "Well, here are $4$ cords of logs, all of the same thickness as before,
 * only they are in $6$-feet lengths, instead of $3$ feet.
 * What will your charge be for cutting them all up into similar $1$-foot lengths?"


 * It is curious that they could not at once agree as to the fair price for the job.
 * What does the reader think the charge ought to be?

Solution
$50$ shillings.

Proof
The workman charges for the number of cuts per log.

A cord is a unit of volume.

$4$ cords of $6$-foot logs is the same number of logs as $2$ cords of $3$-foot logs.

The key point is that:
 * it takes $2$ cuts to cut a $3$-foot log into $1$-foot pieces

but:
 * it takes $5$ cuts to cut a $6$-foot log into $1$-foot pieces.

So the workman should charge:
 * $30 \times \dfrac 2 3 \times \dfrac 5 2 = 50 \shillings$