Question

City Carpet and Flooring advertises that they can install 1,200 square feet of carpet in 2 1/2 hours. Select whether each installation rate has the same unit rate, in square feet per hour, as City Carpet and Flooring.

Yes

No

960 square feet of carpet in 2 hours

1,000 square feet of carpet in 1 3/4 hours

320 square feet of carpet in 2/3 hour

Answer 1

After calculating the unit rates for each scenario, only the installation of 960 square feet in 2 hours has the same unit rate as City Carpet and Flooring, which is 480 square feet per hour.

Step-by-step explanation:

The student's question involves calculating and comparing unit rates of carpet installation to determine if various scenarios have the same unit rate as City Carpet and Flooring, which installs 1,200 square feet in 2 1/2 hours. To compare the unit rates, we need to find the rates in square feet per hour for each scenario.

The unit rate for City Carpet and Flooring is:
1,200 square feet ÷ 2.5 hours = 480 square feet per hour.

Now, for each given scenario we calculate the unit rate:

• 960 square feet ÷ 2 hours = 480 square feet per hour (Yes)
• 1,000 square feet ÷ 1.75 hours = 571.4 square feet per hour (No, this is a faster rate)
• 320 square feet ÷ 0.67 hours = 477.6 square feet per hour (No, this rate is slightly lower)

Only the first scenario has the same unit rate of carpet installation as City Carpet and Flooring.