2025 MGS(S) PRELIMS P2 Q8

A water heater heats water in a tank to \(38^\circ\text{C}\).

1. In the morning, the initial temperature is \(25^\circ\text{C}\), and the heater warms it at \(x^\circ\text{C}\) per minute. Write an expression in \(x\) for the time taken.[1]
2. In the afternoon, the initial temperature is \(28^\circ\text{C}\), and the rate is \((x+2)^\circ\text{C}\) per minute. Write an expression in \(x\) for the time taken.[1]
3. The morning and afternoon heating times differ by 2 minutes. Write an equation in \(x\) and show that it reduces to \(2x^2+x-26=0\).[3]
4. Solve \(2x^2+x-26=0\), giving your answers to 2 decimal places.[3]
5. Find the morning heating time in minutes and seconds, correct to the nearest second.[1]