Leak vs. compensating inflow (capacity from times) A tank has a leak that would empty it in 8 hours. A tap admitting 3 L per minute is turned on, and now the tank empties in 12 hours. What is the capacity of the tank?
Correct Answer: 4320 L
Introduction / Context:This is a capacity-from-rate-difference problem. Treat the leak as a constant outflow and the tap as a constant inflow. The observed emptying time under compensation identifies the net outflow; solving two linear relations yields the tank volume.
Given Data / Assumptions:
- Leak alone empties in 8 h ⇒ leak rate = V/8 per hour = V/480 per min.
- With 3 L/min added, emptying time is 12 h ⇒ net outflow = V/12 per hour = V/720 per min.
- V = tank capacity in liters.
Concept / Approach:Net outflow (leak − 3) equals V/720. Set up the equation using leak-alone rate and solve for V.
Step-by-Step Solution:
Leak rate per min = V/480V/480 − 3 = V/720(V/480 − V/720) = 3 ⇒ V(1/480 − 1/720) = 3V * (1/1440) = 3 ⇒ V = 4320 LVerification / Alternative check:Check: leak 540 L/h; tap 180 L/h in; net 360 L/h ⇒ 4320/360 = 12 h.
Why Other Options Are Wrong:4000, 2250, 4120 do not satisfy both time conditions simultaneously.
Common Pitfalls:Mistaking hours for minutes or mixing units inside the same equation.
Final Answer:4320 L