2026 DSS P2 Q5

Tap A takes \(x\) hours to fill a swimming pool. Tap B fills the same pool 2 hours faster than Tap A. Tap A and Tap B can fill up the swimming pool in 4 hours if they are both turned on together.

1. Write down an equation to represent this information and show that it reduces to \(x^2-10x+8=0\).[3]
2. Solve the equation \(x^2-10x+8=0\), giving your solutions correct to two decimal places.[3]
3. Calculate how long it would take Tap B to fill the tank alone.
   Give your answer in hours and minutes, correct to the nearest minute.[1]