Answer
$t=30.5s$
Work Step by Step
The required time can be determined as follows:
The work done by the man is given as
$U=Wh$
$\implies U=150(15)=2250lb\cdot ft$
The power generated by the man is
$P_m=\frac{U}{t}$
$\implies P_m=\frac{2250}{4}=562.5\times \frac{1}{550}=1.02hp$
Now, the power of the bulb is given as
$P_b=100\times (\frac{550bl\cdot ft/s}{746W})=73.73lb\cdot ft/s$
We know that
$t=\frac{U}{P_b}$
We plug in the known values to obtain:
$t=\frac{2250}{73.73}$
$\implies t=30.5s$
