It takes 7 minutes to fill a bathtub using coldwater faucet alone. It takes 12 minutes using the hot water faucet alone. How long will it take to fill the tub using both?

Fill the bathtub in seven minutes using the cold water faucet.

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To find out how long it will take to fill the tub using both faucets, we can use the concept of rates.

Let's denote the rate at which the cold water faucet fills the tub as ( C ) (in tubs per minute) and the rate at which the hot water faucet fills the tub as ( H ) (in tubs per minute).

We can express the rates as:

[ C = \frac{1}{7} \text{ tubs/minute} ] [ H = \frac{1}{12} \text{ tubs/minute} ]

The combined rate when both faucets are open is the sum of their individual rates:

[ C + H = \frac{1}{7} + \frac{1}{12} ]

To add these fractions, we need to find a common denominator, which is ( 84 ):

[ C + H = \frac{12}{84} + \frac{7}{84} ] [ C + H = \frac{19}{84} \text{ tubs/minute} ]

Now, to find out how long it will take to fill the tub using both faucets, we can use the formula:

[ \text{Time} = \frac{\text{Amount}}{\text{Rate}} ]

Where the amount is 1 tub, and the rate is the combined rate ( C + H ):

[ \text{Time} = \frac{1}{\frac{19}{84}} ] [ \text{Time} = 1 \times \frac{84}{19} ] [ \text{Time} = \frac{84}{19} \text{ minutes} ]

Therefore, it will take approximately ( \frac{84}{19} ) minutes to fill the tub using both faucets. This is approximately 4.421 minutes or 4 minutes and 25.3 seconds.