2025 YCKSS PRELIMS P2 Q6

A motorboat travels at \(x\) km/h in still water. Its speed is \(x-3\) km/h upstream and \(x+3\) km/h downstream. It travels 12 km from A to B upstream, then 9 km from B to C downstream, taking 1 hour 15 minutes in total.

1. Show that \(5x^2-84x-81=0\).[5]
2. Solve \(5x^2-84x-81=0\), giving answers correct to two decimal places.[3]
3. Explain why one answer must be rejected.[1]
4. Calculate the difference between the two journey times in minutes and seconds, to the nearest second.[2]