Answer
The nurse has an average speed of $0.17\,\mathrm{m/s}.$
Work Step by Step
Total distance traveled, $d=25+25=50\,\mathrm{m}$.
Total time taken, $t=0.5+4+0.5=5\,\mathrm{min}=300\,\mathrm{s}$.
Average speed,
\begin{align*}
s&=\frac{d}{t}=\frac{50}{300}\\&=0.17\,\mathrm{m/s}
\end{align*}