Henry Ernest Dudeney/Puzzles and Curious Problems/67 - Carrying Bags/Solution

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Puzzles and Curious Problems by Henry Ernest Dudeney: $67$

Carrying Bags
A gentleman had to walk to his railway station, four miles from his house,
and was encumbered by two heavy bags of equal weight, but too heavy for him to carry alone.
His gardener and the boy both insisted on carrying the luggage;
but the gardener is an old man, and the boy not sufficiently strong,
while the gentleman believes in a fair division of labour, and wished to take his own share.
They started off with the gardener carrying one bag and the boy the other,
while the gentleman worked out the best way of arranging that the three should share the burden equally among them.
Now, how would you have managed it?


Solution

Let the boy carry his one bag for $1 \tfrac 1 3$ miles.

Then let him hand it to the gentleman, who will carry it to the station.

Let the gardener carry the other bag for $2 \tfrac 2 3$ miles.

Then let him hand it to the boy, who will then carry it to the station.

Each of the $3$ people have then carried one bag for $2 \tfrac 2 3$ miles.


Whether this is equal division of labour is debatable, because:

the gardener is free to walk back home after having walked only $2 \tfrac 2 3$ miles, while the boy has to walk the entire journey
the gentleman has to walk only one direction, while the others have to walk the $4$ miles home again.

However, while in modern times walking is considered a burdensome chore, it was just the way people got about a century ago, and not considered "labour".


Sources

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