1. **State the problem:** A girl pushes her brother's sled with a force of 300 N over a distance of 750 m. We want to find the work done by the girl considering the force of friction acting against the motion. 2. **Recall work formula:** Work is defined as the net force applied multiplied by the distance moved in the direction of the force. Mathematically, $$W = F_{net} \times d$$ where $$F_{net}$$ is the net force and $$d$$ is the distance. 3. **Calculate net force:** The net force is the applied force minus the force of friction since friction opposes the motion. (a) When friction is 200 N, $$F_{net} = 300 - 200 = 100\,N$$ (b) When friction is 300 N, $$F_{net} = 300 - 300 = 0\,N$$ 4. **Calculate work done:** Using $$W = F_{net} \times d$$ with $$d = 750\,m$$, (a) $$W = 100 \times 750 = 75,000\,J$$ (b) $$W = 0 \times 750 = 0\,J$$ **Final answers:** - (a) The work done is $$75,000\,J$$. - (b) The work done is $$0\,J$$ because the net force is zero.