2025 GESS PRELIMS P2 Q9

Ali and Robert participated in a \(42\text{ km}\) running event. Ali completed the race with an average speed of \(x\text{ km/h}\). Robert completed the race at an average speed of \(2\text{ km/h}\) slower than Ali.

1. Given that Robert completed the race 30 minutes later than Ali, form an equation in \(x\) and show that it reduces to \(x^2-2x-168=0\).[4]
2. Solve the equation \(x^2-2x-168=0\).[2]
3. Explain why one of the solutions in (b) must be rejected.[1]
4. Calculate the time taken for Robert to complete the race.[1]