Final answer:
The total external work done on the system of Jonathan and his bicycle as they travel up a hill is determined by the net work of all external forces, with the work done by gravity being positive since it acts in the direction of their upward displacement.
Step-by-step explanation:
Regarding the total external work done on the system of Jonathan and the bicycle as they travel up a hill, we can determine this by considering the net work done by all external forces. When Jonathan and his bicycle move up the hill against gravity, work is done by gravity since it has a component in the direction of their motion. The work done by gravity on Jonathan and the bicycle is positive because the gravitational force and the displacement act in the same direction (weight points down but the net vertical displacement is upward up the hill).
On the other hand, any other forces, such as friction or a force applied by Jonathan to the pedals, could also contribute to the total external work. The work done by other external forces depends on the specific details of the problem, such as the amount of friction and how much force Jonathan applies. The total external work done on the system is the sum of the work done by each of these forces.