Two pipes A and C can fill a tank in 10 hours and 15 hours respectively. If A is open all the time and C is open for 30 minutes, then find the time needed for the tank to be filled.

Given:

Pipe A fills tank in 10 hours.

Pipe C fills tank in 15 hours.

Pipe C is open for 30 minutes = 0.5 hours

Let Pipe A be open for t hours.

Formula Used:

Work done = Rate x Time

Rate of Pipe A = 1/10 (tank/hour)

Rate of Pipe C = 1/15 (tank/hour)

Calculation:

Part of tank filled by Pipe C in 0.5 hours = (1/15) x 0.5

⇒ Part filled by C = 1/30

Remaining part of tank to be filled by Pipe A = 1 - 1/30

⇒ Remaining part = 29/30

Time taken by Pipe A to fill 29/30 part of tank = (29/30) / (1/10)

⇒ Time for A = (29/30) x 10 = 29/3 hours

Total time needed = Time for A

⇒ Total time = 29/3 hours = \(9\frac{2}{3} \text{ hours}\)

∴ The time needed for the tank to be filled is \(9\frac{2}{3} \text{ hours}\).