Final answer:
When both the cold water faucet (fill rate of 1/9 of the tub per minute) and the hot water faucet (fill rate of 1/11 of the tub per minute) are running together, they have a combined fill rate of 20/99 of the tub per minute. Consequently, the bathtub will be filled in 4.95 minutes with both faucets running simultaneously.
Step-by-step explanation:
To solve the problem about how long it will take to fill the tub with both faucets running together, we first need to find out how much of the tub each faucet can fill in one minute. We can consider the rate at which each faucet fills the tub to be a fraction of the tub per minute.
The cold water faucet fills the tub in 9 minutes, so its rate is 1/9 of the tub per minute. The hot water faucet fills the tub in 11 minutes, which means its rate is 1/11 of the tub per minute. When both faucets are running together, their rates are additive.
So, the combined rate of both faucets is (1/9) + (1/11). To find their combined rate, we need the least common denominator, which is 99. So we convert the rates: (11/99) for the cold water faucet + (9/99) for the hot water faucet, which is 20/99 of the tub per minute.
To find out how many minutes it will take to fill the entire tub with both faucets running, we take the reciprocal of the combined rate: 99/20 minutes. Therefore, the tub will be filled in 4.95 minutes when both faucets are used together.