Propositiones ad Acuendos Juvenes/Problems/52 - De Homine Patrefamilias

by : Problem $52$

 * De Homine Patrefamilias: A Lord of the Manor
 * A man ordered that $90$ measures of grain were to be moved from one of his houses to another, $30$ leucas away.
 * One camel was to carry the grain in $3$ journeys, carrying $30$ measures on each journey.
 * ''The camel eats one measure for each leuca.
 * How many measures will remain?

Solution
$20$ measures.

Proof
On the $1$st journey, the camel carries $30$ measures over $20$ leucas, eating $1$ measure for each leuca, leaving $10$ leucas.

On the $2$nd journey, the camel likewise carries $30$ measures over $20$ leucas, eating $1$ measure for each leuca, leaving $10$ leucas.

On the $3$rd journey, the camel again carries $30$ measures over $20$ leucas, eating $1$ measure for each leuca, leaving $10$ leucas.

Now he is at the point $10$ leucas away, with $30$ measures to take over $10$ leucas.

During that journey the camel eats $10$ measures, leaving $20$ measures.