Two pipes fill a tank in 20 min and 24 min; a waste pipe empties at 3 gallons/min. All three together fill the tank in 15 min. What is the tank's capacity (in gallons)?

Problem restatementGiven two fill rates dependent on capacity and one constant emptying rate, find the capacity from the net fill time.

Given data

• Fillers: V/20 and V/24 gallons per min
• Waste: 3 gallons per min
• Net fill time with all open: 15 min ⇒ net rate = V/15

Concept/ApproachSet up the net-rate equation: V/20 + V/24 − 3 = V/15 and solve for V.

Step-by-step calculationV/20 + V/24 = (6V + 5V)/120 = 11V/12011V/120 − 3 = V/15 = 8V/120(11V − 8V)/120 = 3 ⇒ 3V/120 = 3 ⇒ V/40 = 3V = 120 gallons

Verification/AlternativeRates at V = 120: 6 + 5 − 3 = 8 gal/min ⇒ 120/8 = 15 min (checks).

Common pitfallsForgetting that only the waste pipe's rate is capacity-independent.

Final Answer120 gallons