Leak and inlet together determine capacity: A leak at the bottom of a tank can empty the full tank in 6 h. An inlet pipe can fill water at 4 L per minute. With the tank initially full, the inlet is opened and, due to the leak, the tank becomes empty in 8 h. What is the capacity of the tank (in liters)?

Introduction / Context:
When a leak and an inlet operate simultaneously, the net rate decides whether the tank level rises or falls. With the tank starting full and eventually emptying, the leak dominates the combined effect. We can model both in consistent “tank-per-hour” units using the unknown capacity to link the inlet’s liters per hour to a fraction of the tank per hour.

Given Data / Assumptions:

• Leak empties a full tank in 6 h ⇒ leak rate L = 1/6 tank/h (outflow).
• Inlet flow = 4 L/min = 240 L/h.
• Starting full, after opening inlet, the tank empties in 8 h ⇒ net rate = −1/8 tank/h.
• Capacity = V liters (unknown).

Concept / Approach:
Express the inlet as a fraction of a tank per hour: inlet rate = 240/V tank/h. The net rate is inlet minus leak, and equals −1/8 tank/h. Solve for V from 240/V − 1/6 = −1/8.

Step-by-Step Solution:

Verification / Alternative check:
Inlet as fraction: 240/5760 = 1/24 tank/h. Net = 1/24 − 1/6 = 1/24 − 4/24 = −3/24 = −1/8 tank/h ⇒ the full tank empties in 8 h, consistent.

Why Other Options Are Wrong:
Values like 5670 L or 5700 L would not satisfy the precise balance 240/V = 1/24, leading to a different emptying time.

Common Pitfalls:
Mixing liters per hour and tank fractions without introducing the tank capacity V, or assuming the tank must fill because the inlet is open. The sign of the net rate determines the direction.

Final Answer:
5760 L