Average speed for an outward and return journey

A cyclist rides \(d\) km from home to a park at a constant \(u\) km/h and returns along the same route at a constant \(v\) km/h.

1. Show that the average speed for the whole journey is \(\dfrac{2uv}{u+v}\) km/h.[3]
2. The cyclist rides to the park at \(15\) km/h. Find the return speed needed for an average speed of \(20\) km/h.[2]
3. Explain why no return speed can give an average speed of \(30\) km/h when the outward speed is \(15\) km/h. State one assumption of the model.[3]