Question

Left on together, the cold and hot water faucets of a certain bathtub take 5 minutes to fill the tub. If it takes the cold water faucet 15 minutes to fill the tub by itself, how long will it take the hot water faucet to fill the tub on its own? Do not do any rounding.

Answer 1

Answer:
`7.5\ minutes`

Explanation:

You need to apply the following formula:

`(1)/(T_A)+(1)/(T_B)=(1)/(T_T)`

Where
`T_A` is the individual time for object A (In this case, cold water faucet),
`T_B` is the individual time for object B ( (In this case the hot water faucet) and
`T_T` is the time for A and B together.

So, you can identify that:

`T_A=15\\T_T=5`

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
`T_B`.

Therefore, you get the following result:

`(1)/(15)+(1)/(T_B)=(1)/(5)\\\\(1)/(T_B)=(1)/(5)-(1)/(15)\\\\(1)/(T_B)=(2)/(15)\\\\1=((2)/(15))(T_B)\\\\(15)/(2)=T_B\\\\T_B=7.5`