It takes the cold water faucet times as long to fill a bathtub as it does the hot water faucet. Left on together, the cold and hot water faucets take minutes to fill the tub. How long will it take the hot water faucet to fill the tub by itself?

Question:

It takes the hot water faucet 4 times as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and hot water faucets take 3 minutes to fill the tub. How long will it take the cold water faucet to fill the tub by itself?

The answer to the question is

It take the hot water faucet 15 minutes to fill the tub by itself.

Step-by-step explanation:

Time to fill the bathtub by the hot water faucet = 4×Time to fill the bathtub by the hot water faucet

Let the time of the hot water faucet to fill the bathtub = H

Let the time of the cold water faucet to fill the bathtub = C

Therefore H = 4×C

Let the flow rate of the hot water faucet = h

Let the flow rate of the hot water faucet = c

To fill the bath tub we have (h + c)×t  = B m³

Where B = volume of the bathtub

Then (h + c)×3 = B gives

but c = 4×h so we have

( h + 4·h)3 = B or 15·h =B

Therefore it will take 15 minutes for the water faucet to fill the bathtub.