A cistern can be filled by an inlet pipe in 4 hours, but due to a leak at the bottom, it...
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A cistern can be filled by an inlet pipe in 4 hours, but due to a leak at the bottom, it takes 6 hours to fill completely. How long will the leak alone take to empty the full cistern?
Show answer & explanation
The net filling rate is the difference between the inlet pipe's rate and the leak's emptying rate. By calculating the difference between the ideal filling rate (1/4) and the actual filling rate (1/6), we find the rate at which the leak empties the cistern.
Step-by-step Derivation:
Step 1: Define the rate of the inlet pipe. The inlet pipe fills the cistern in 4 hours, so its rate is 1/4 of the cistern per hour.
Step 2: Define the net rate of filling with the leak. With the leak active, the cistern fills in 6 hours, so the net rate is 1/6 of the cistern per hour.
Step 3: Set up the equation for the net rate. Let 'L' be the time taken by the leak to empty the cistern. The rate of the leak is 1/L.
Net Rate = Inlet Rate - Leak Rate
1/6 = 1/4 - 1/L
Step 4: Solve for 1/L.
1/L = 1/4 - 1/6
To subtract these fractions, find a common denominator (12):
1/L = 3/12 - 2/12
1/L = 1/12
Step 5: Calculate L.
L = 12 hours.