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Left on together, the cold and hot water faucets of a certain bathtub take 7 minutes to fill the tub. If it takes the hot water faucet 17 minutes to fill the tub byItself, how long will it take the cold water faucet to fill the tub on its own?Do not do any rounding.

Left On Together The Cold And Hot Water Faucets Of A Certain Bathtub Take 7 Minutes To Fill The Tub If It Takes The Hot Water Faucet 17 Minutes To Fill The Tub class=

Sagot :

Given that:

Time to fill the bathtub with both the cold and hot water faucets = 7 minutes

Time to fill the bathtub only with the hot water faucet = 17 minutes

Find the time to fill the bathtub only with the cold water faucet.

Let the cold water faucet will take x minutes to fill the tab. Then

[tex]\frac{1}{x}+\frac{1}{7}=\frac{1}{17}[/tex]

Solve for x.

[tex]\begin{gathered} \frac{1}{x}=\frac{1}{17}-\frac{1}{7} \\ =\frac{17-7}{119} \\ =\frac{10}{119} \\ x=\frac{119}{10} \\ =11.9\text{ minutes} \end{gathered}[/tex]

Cold water faucet will take 11.9 minutes to fill the tub.

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