Final answer:
1100 sq ft of carpet in 2 hours is equivalent to 1,925 sq ft of carpet in 3 1/2 hours.
Step-by-step explanation:
To determine if 1100 sq ft of carpet in 2 hours is equivalent to 1,925 sq ft of carpet in 3 1/2 hours, we need to calculate the rate at which carpet is being installed in both scenarios.
In the first scenario, the rate of carpet installation is:
1100 sq ft / 2 hours = 550 sq ft/hour.
In the second scenario, the rate of carpet installation is:
Using the concept of unit rate and cross multiplication, we can calculate the equivalent rate:
1,925 sq ft / 3.5 hours = 550 sq ft / x hours.
Cross multiplying, we get:
1,925 * x = 550 * 3.5.
Simplifying, we find:
x = (550 * 3.5) / 1,925 = 1000 / 1.925 = 519.48 hours.
Therefore, the rates of carpet installation in both scenarios are equivalent.