To find the missing values in the table, let's analyze the relationship between the square footage and the cleaning time.
From the data provided:
- For 10 square feet, it takes 4 minutes.
- For 70 square feet, we need to find the cleaning time.
- For an unknown number of square feet, it takes 48 minutes.
- For 210 square feet, it takes 84 minutes.
Now, let's find the rates between the known values.
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From 10 to 70 square feet (60 square feet increase):
- Cleaning time goes from 4 minutes to an unknown value.
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From 70 to 210 square feet (140 square feet increase):
- Cleaning time goes from an unknown value to 84 minutes.
Next, we calculate feet per minute based on the given points:
For 10 to 210 square feet, we know:
- From 10 to 210: \( 210 - 10 = 200 \) square feet
- From 4 to 84 minutes: \( 84 - 4 = 80 \) minutes
Now, we can find the average rate of cleaning per square foot across this entire range:
Average rate = \(\frac{80 \text{ minutes}}{200 \text{ square feet}} = 0.4 \text{ minutes per square foot}\)
Using this average to estimate cleaning times for the known ranges:
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For 70 square feet: \[ 70 \text{ square feet} \times 0.4 \text{ minutes/sq ft} = 28 \text{ minutes} \]
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The square footage corresponding to 48 minutes can be calculated: \[ 48 \text{ minutes} = 0.4 \text{ minutes/sq ft} \times x \text{ square feet} \] Solving for \( x \): \[ x = \frac{48 \text{ minutes}}{0.4 \text{ minutes/sq ft}} = 120 \text{ square feet} \]
So now we can fill in the table:
- Number of Square Feet: 10, 70, 120, 210
- Time in Minutes: 4, 28, 48, 84
The completed table is:
| Number of Square Feet | Time in Minutes | |-----------------------|------------------| | 10 | 4 | | 70 | 28 | | 120 | 48 | | 210 | 84 |
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