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In an effort to improve student performance, teachers at $12$ city schools are being asked to work a longer day next year for a relatively small increase in salary. For working an additional $190 \mathrm{~h}$, a teacher currently earning $\$ 79,400$ per year would see his or her salary increase to $\$ 83,500$ per year.

From the information given above, find the hourly rate the teachers will be paid for the extra hours they will work.

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