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.