A Game of Cat and Mouse

A mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot.  The mouse descends $\frac{1}{2}$ a braccia a day and at night it turns back $\frac{1}{6}$ of a braccia.  The cat climbs one braccia a day and goes back $\frac{1}{4}$ of a braccia each night.  The tree grows $\frac{1}{4}$ of a braccia between the cat and the mouse each day and it shrinks $\frac{1}{8}$ of a braccia every night.  In how many days will the cat reach the mouse?

Summa de arithmetica, Luca Pacioli, 1494

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