Question

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 10 70 __ 210
Time in Minutes 4 __ 48 84


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Answer 1

To find the missing values in the table, we can analyze the given data points. The relationship between the number of square feet and the time in minutes can be examined to see if there's a consistent ratio.

The data provided is:

- 10 square feet = 4 minutes
- 70 square feet = __ minutes
- __ square feet = 48 minutes
- 210 square feet = 84 minutes

### Step 1: Calculate cleaning time per square foot
From the data provided, we can determine the cleaning rate for the known values:

For **10 square feet**:
\[
Cleaning \, rate = \frac{4 \, minutes}{10 \, square \, feet} = 0.4 \, minutes/square \, foot
\]

For **210 square feet**:
\[
Cleaning \, rate = \frac{84 \, minutes}{210 \, square \, feet} = 0.4 \, minutes/square \, foot
\]

It appears that the cleaning rate is consistent at **0.4 minutes per square foot**.

### Step 2: Use the rate to find the missing times
Using the cleaning rate, we can now calculate the missing times.

1. **For 70 square feet**:
\[
Time = 70 \, square \, feet \times 0.4 \, minutes/square \, foot = 28 \, minutes
\]

2. **For the square footage that takes 48 minutes**:
Let \( x \) be the number of square feet.
\[
48 \, minutes = x \, square \, feet \times 0.4 \, minutes/square \, foot
\]
\[
x = \frac{48}{0.4} = 120 \, square \, feet
\]

### Completed Table:
Now we can complete the table:

| Number of Square Feet | 10 | 70 | 120 | 210 |
|-----------------------|----|----|-----|-----|
| Time in Minutes | 4 | 28 | 48 | 84 |

Thus, the missing values are:
- **70 square feet** takes **28 minutes**.
- **120 square feet** takes **48 minutes**.