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)

Square Feet and Cleaning Time

Number of Square Feet 50 80 Response area 160
Time in Minutes 20 Response area 40 64

1 answer

Based on the provided data about the number of square feet and the cleaning time, we can summarize the cleaning times for the designated areas as follows:

  • 50 square feet: 20 minutes
  • 80 square feet: 40 minutes
  • 160 square feet: 64 minutes

This data indicates that the cleaning time increases as the number of square feet increases. It suggests a linear relationship between the area to be cleaned and the time taken, which can be analyzed further.

Possible Calculations:

  1. Time per square foot:

    To find the time taken per square foot, we can calculate it for each of the given areas:

    • For 50 square feet: \( \frac{20 \text{ minutes}}{50 \text{ sq ft}} = 0.4 \text{ minutes/sq ft} \)
    • For 80 square feet: \( \frac{40 \text{ minutes}}{80 \text{ sq ft}} = 0.5 \text{ minutes/sq ft} \)
    • For 160 square feet: \( \frac{64 \text{ minutes}}{160 \text{ sq ft}} = 0.4 \text{ minutes/sq ft} \)
  2. Linear Relationship:

    We can also examine this data to determine a possible equation for cleaning time based on square footage. By finding the slope between points, we can derive a formula.

    For example, from 50 sq ft to 80 sq ft, the increase in area is 30 sq ft, and the increase in time is 20 minutes, which gives us a rate:

    \[ \text{Slope} = \frac{40 - 20}{80 - 50} = \frac{20}{30} = \frac{2}{3} \text{ minutes per sq ft} \]

    This can also lead to creating a function like \( T = k \cdot A \), where \( T \) is time, \( A \) is area, and \( k \) is the constant of proportionality.

Overall, the data you provided is enough to draw conclusions and perform calculations about the cleaning service's time efficiency regarding different home sizes. If you need further analysis or specific calculations, please let me know!