Answer: [tex]7.5\ minutes[/tex]
Step-by-step explanation:
You need to apply the following formula:
[tex]\frac{1}{T_A}+\frac{1}{T_B}=\frac{1}{T_T}[/tex]
Where [tex]T_A[/tex] is the individual time for object A (In this case, cold water faucet), [tex]T_B[/tex] is the individual time for object B ( (In this case the hot water faucet) and [tex]T_T[/tex] is the time for A and B together.
So, you can identify that:
[tex]T_A=15\\T_T=5[/tex]
Therefore, in order to find how long it will take for the hot water faucet to fill the tub on its own, you need to:
1. Substitute the known values into the formula.
2. Solve for [tex]T_B[/tex].
Therefore, you get the following result:
[tex]\frac{1}{15}+\frac{1}{T_B}=\frac{1}{5}\\\\\frac{1}{T_B}=\frac{1}{5}-\frac{1}{15}\\\\\frac{1}{T_B}=\frac{2}{15}\\\\1=(\frac{2}{15})(T_B)\\\\\frac{15}{2}=T_B\\\\T_B=7.5[/tex]
