Exercise $9-11($Algo$)$ Working Backwards from Labor Variances $[$LO$9-5]$

The auto repair shop of Quality Motor Company uses standards to control the labor time and labor cost in the shop. The standard labor cost for a motor tune$-$up is given below:

Standard Hours Standard Rate Standard Cost

Motor tune$-$up $2\mathrm{.}50$ $ $31\mathrm{.}00$ $ $77\mathrm{.}50$

The record showing the time spent in the shop last week on motor tune$-$ups has been misplaced. However, the shop supervisor recalls that $56$ tune$-$ups were completed during the week, and the controller recalls the following variance data relating to tune$-$ups:

Labor rate variance $ $146$ F

Labor spending variance $ $102$ U

Required:

$1.$ Determine the number of actual labor$-$hours spent on tune$-$ups during the week.

$2.$ Determine the actual hourly rate of pay for tune$-$ups last week. $($Round your answer to $2$ decimal places.$)$