Answer
4.2 m.
Work Step by Step
The table on page 901 shows that the Relative Biological Effectiveness (RBE) of gamma rays is 1. The allowed dose in rem is the same as the dose in rad. Convert the units of the allowed dose to rad/hour.
$$\frac{5.0rem}{year}\frac{1rad}{1rem}\frac{year}{52weeks}\frac{1week}{35h}=2.747\times10^{-3}\frac{rad}{h}$$
The radiation intensity falls off as $1/r^2$ (the inverse square of the distance). Therefore, the dose rate multiplied by $r^2$ is constant.
$$(2.747\times10^{-3}\frac{rad}{h})r^2=(4.8\times10^{-2}\frac{rad}{h})(1m)^2$$
$$r=\sqrt{\frac{(4.8\times10^{-2}\frac{rad}{h})(1m)^2}{(2.747\times10^{-3}\frac{rad}{h})}}\approx 4.2m$$
At that distance from the source, working 35 hours per week, a worker will receive a dose of 5.0 rem/year.
