A cold water faucet can fill the bathtub in 12 minutes, and a hot water faucet can fill the bathtub in 18 minutes. The drain can empty the bathtub in 24 minutes. If both faucets are on and the drain is open, how long would it take to fill the bathtub?

It will take 10.3 minutes to fill the bathtub.

Step-by-step explanation:

Let us call the volume of the bathtub , and ,, and the flow rates of cold water, hot water, and the drain respectively.

The cold water faucet fills the bathtub in 12 minutes; therefore,

(1). .

Similarly, for the hot water faucet

(2).

and for the drain

(3). .

If the drain and the faucets are turned on together, then we have:

(this says water flow after time must equal )

Now, from equations (1), (2), and (3) we substitute the values of , , and to get:

by simplifying the left side we get:

Thus, if both faucets are on and the drain is open, it will take 10.3 minutes to fill the bathtub.

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step-by-step explanation: