Answer
a) $W=-30kJ$
b) The resistive force is not a conservative force.
Work Step by Step
a) The work done by the round trip is $W=W_{go}+W_{return}$
In both the going and return trips, the resistive force $R=3N$ acts on the bicyclist for $s=5km=5\times10^3m$ and opposes the motion, so $\theta=180^o$. Therefore, $$W_{go}=W_{return}=(R\cos\theta)s=-1.5\times10^4J$$
This means $$W=W_{go}+W_{return}=-3\times10^4J=-30kJ$$
b) The resistive force is not a conservative force because while the round trip is a closed path, the net work done on the bicyclist by the resistive force does not equal $0$, contrary to the definition of a conservative force.
