Question

Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the cold water faucet 12 minutes to fill the tub by itself, how long will it take the hot water faucet to fill the tub on its own

Answer 1

When both facets are turned on, they fill 1%2F4 of the bathtub volume per minute.

When only cold facet is turned on, it fills 1%2F12 of the bathtub volume per minute.

It means that the contribution of the hot facet is the difference 1%2F4 - 1%2F12 = 3%2F12 - 1%2F12 = 2%2F12 = 1%2F6 of the bathtub volume per minute.

Therefore, it will take 6 minutes for the hot facet to fill the bathtub working alone.