SOLUTION: A faucet can deliver water rapidly than a drain can remove it. IF the sink is empty, the drain and the faucet is opened then the sink fills in 4 minutes. The drain is able to empty

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Question 196788: A faucet can deliver water rapidly than a drain can remove it. IF the sink is empty, the drain and the faucet is opened then the sink fills in 4 minutes. The drain is able to empty a full sink in 2 minutes longer than the faucet can fill the sink when the drain is closed. What are the tines needed far each to fill or drain if it works alone?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Let t represent the number of minutes required for the faucet to fill the sink with the drain closed. Then t + 2 represents the number of minutes it takes the drain to empty a full sink. Then the faucet can fill of the sink in 1 minute, and the drain can empty of the sink in 1 minute, and working together they fill of the sink in 1 minute.

So:



LCD is the product of the denominators: , so:



Multiply both sides by and collect terms on the left:



Solve the quadratic, excluding the negative root (the sink certainly didn't fill before you turned the water on) to get the time it takes the faucet to fill the sink. Add 2 to get the time for the drain.

John