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?
Answer:
The answer to the question is
It take the hot water faucet 15 minutes to fill the tub by itself.
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.