Which inequality can be used to determine the number of minutes after which the amount of cold water Celia put into the bathtub is greater than the amount of hot water she put into the bathtub?

Question

Celia put hot and cold water into a bathtub. For the first two minutes she added hot water to the bathtub. After two minutes, she added both hot and cold water to the bathtub. The hot water flows at the rate of 2.2 gallons per minute. The cold water flows at the rate of 3.4 gallons per minute. Let t represent the number of minutes Celia put cold water into the bathtub. Which inequality can be used to determine the number of minutes after which the amount of cold water Celia put into the bathtub is greater than the amount of hot water she put into the bathtub?

help I don’t understand I’m about to give up

Answer 1

Let H be the amount of hot water in the tub. Hot water flows at a rate of 2.2 g/m. We let it run alone for 2 minutes, so that puts (2.2 g/m)(2 m) = 4.4 gallons of hot water in the tub before we even turn on the cold water. Now we turn on the cold water along with the hot. After t minutes, the amount of hot water in the tub is:

H = 4.4 + (2.2)t

The amount of cold water, C, is:

C = (3.4 g/m)t

We want C ≥ H (gallons of of cold water greater than or equal to the gallons of hot water)

3.4t ≥ 4.4 + 2.2t

Solve for t. The units of t are minutes.