2025 SST PRELIMS P2 Q3

Two taps, \(X\) and \(Y\), together fill a tank in 6 hours. Tap \(X\) takes \(x\) hours to fill it alone. Tap \(Y\) takes 25 hours less than tap \(X\) to fill it alone.

1. Write an expression in terms of \(x\) for the fraction of the tank tap \(X\) fills in one hour.[1]
2. Write an expression in terms of \(x\) for the fraction of the tank tap \(Y\) fills in one hour.[1]
3. Write an equation for the combined filling rate and show that it reduces to \(x^2-37x+150=0\).[3]
4. Solve \(x^2-37x+150=0\), giving your answers correct to three significant figures.[2]
5. Calculate how long tap Y takes to fill the empty tank. Give your answer in hours and minutes, to the nearest minute.[3]