A home cleaning service takes more time to clean larger spaces. The table shows the number of minutes it takes for the service to clean a certain number of square feet within a home.(2 points)

Question

Square Feet and Cleaning Time
Number of Square Feet: 50 80 ? 160
Time in Minutes: 20 ? 40 64
Responses:
500
32
64
80
10
100
40

Answer 1

To solve for the missing cleaning time corresponding to 80 square feet, we need to analyze the relationship between the square footage and the cleaning time using the provided data:

• 50 square feet takes 20 minutes.
• 80 square feet takes ? minutes.
• 160 square feet takes 64 minutes.

We can look for a consistent rate of cleaning time per square foot.

From the data, we can calculate the rate of time per square foot for the known values:

1. For 50 square feet: \[ \text{Rate} = \frac{20 \text{ minutes}}{50 \text{ square feet}} = 0.4 \text{ minutes per square foot} \]

2. For 160 square feet: \[ \text{Rate} = \frac{64 \text{ minutes}}{160 \text{ square feet}} = 0.4 \text{ minutes per square foot} \]

Now we can use the same rate to calculate the time for 80 square feet: \[ \text{Time for 80 square feet} = 80 \text{ square feet} \times 0.4 \text{ minutes per square foot} = 32 \text{ minutes} \]

Therefore, the missing time for cleaning 80 square feet is 32 minutes.