A master carpenter planes $21\mathrm{pieces}$ of wood in a day. His apprentice planes $2\mathrm{pieces}$ per hour and worked for several hours during the day. If the difference between the number of pieces of wood planed by the master and the number of pieces planed by the apprentice, divided by $17$, equals $\frac{5}{17}$, how many hours did the apprentice work during the day?

The apprentice worked for