Pipes A and B can fill a tank in 15 hours and 25 hours, respectively, whereas pipe C can empty the full tank in 40 hours. All three pipes are opened together, but pipe A is closed after 5 hours. After how many hours will the remaining part of the tank be filled?

Question

Accepted Answer

Step 1: Calculate the rates of pipes A, B, and C.
- Pipe A fills the tank in 15 hours, so rate of A = 1/15 tank/hour.
- Pipe B fills the tank in 25 hours, so rate of B = 1/25 tank/hour.
- Pipe C empties the tank in 40 hours, so rate of C = -1/40 tank/hour (negative because it empties).

Step 2: Calculate the combined rate when all three pipes are open.
Combined rate = (1/15) + (1/25) - (1/40)
Find common denominator: 600
(1/15) = 40/600, (1/25) = 24/600, (1/40) = 15/600
Combined rate = (40 + 24 - 15)/600 = 49/600 tank/hour

Step 3: Calculate how much of the tank is filled in the first 5 hours with all three pipes open.
Amount filled = rate × time = (49/600) × 5 = 245/600 = 49/120 tank

Step 4: Remaining tank to be filled = 1 - 49/120 = (120/120) - (49/120) = 71/120 tank

Step 5: After 5 hours, pipe A is closed. Now only pipes B and C are open.
Combined rate of B and C = (1/25) - (1/40)
Common denominator = 200
(1/25) = 8/200, (1/40) = 5/200
Combined rate = (8 - 5)/200 = 3/200 tank/hour

Step 6: Time to fill remaining 71/120 tank at rate 3/200 tank/hour:
Time = (71/120) ÷ (3/200) = (71/120) × (200/3) = (71 × 200) / (120 × 3) = 14200 / 360 = 395/10 = 39.5 hours

Answer

Answer

Answer