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 determine the missing values in the cleaning time based on the square footage, we can analyze the data provided.

1. For 50 square feet, it takes 20 minutes.
2. For 80 square feet, we need to find the corresponding time.
3. For the unknown area denoted by "?", we need to calculate its cleaning time.
4. For 160 square feet, it takes 64 minutes.

We can observe that as the area increases, the cleaning time also increases.

Let's first calculate the cleaning rates using the provided data:

• For 50 square feet: 20 minutes → the rate is \( \frac{20 \text{ minutes}}{50 \text{ square feet}} = 0.4 \text{ minutes/square foot} \)
• For 160 square feet: 64 minutes → the rate is \( \frac{64 \text{ minutes}}{160 \text{ square feet}} = 0.4 \text{ minutes/square foot} \)

Since the cleaning rate is consistent at \( 0.4 \) minutes per square foot, we can use this rate to find the missing values.

Now let's calculate the cleaning time for 80 square feet:

\[ \text{Time for 80 square feet} = 80 \text{ square feet} \times 0.4 \text{ minutes/square foot} = 32 \text{ minutes} \]

For the unknown cleaning area (let's denote it as \( x \)):

Since we have already established a constant cleaning rate and previously filled out that \( 160 \) square feet takes \( 64 \) minutes, which also confirms our rate.

So the missing area (the question mark) doesn't appear in the given values. It might suggest checking values. Let's check via interpolation since the only missing figure is that its cleaning time 80 insinuates \( 32 \) minutes to solve \(? = 80\). We just confirmed also similarly that the total cleaning time must be \( x \).

Thus, we have:

• \( 50 \) square feet → \( 20 \) minutes
• \( 80 \) square feet → \( 32 \) minutes
• The next logical could see that it approaches to \( 120 \) square feet → will be next indication we assume possibly give a \( 40 \) (for correlation since \(160\) correspondingly mirrors)

Hence the missing data matches thus correlatively confirms:

So:

• Cleaning time for \( 50 , \text{sq ft} = 20 , \text{min}\)
• Cleaning time for \( 80 , \text{sq ft} = 32 , \text{min}\) (which is the answer)
• Cleaning time for \(160 , \text{sq ft} = 64, \text{min}\)

Therefore, the missing time for 80 should be 32 minutes.

Answer 2

fill in both the blanks in the question

Answer 3

Let's summarize the information provided and fill in both blanks:

Given Data:

• Number of Square Feet:
  • 50 → 20 minutes
  • 80 → ?
  • ? → 40 minutes
  • 160 → 64 minutes

Known Calculations:

1. Cleaning Rate:
   • For 50 sq ft → 20 minutes: \[ \text{Rate} = \frac{20 \text{ min}}{50 \text{ sq ft}} = 0.4 \text{ min/sq ft} \]
   • For 160 sq ft → 64 minutes: \[ \text{Rate} = \frac{64 \text{ min}}{160 \text{ sq ft}} = 0.4 \text{ min/sq ft} \]

Filling in the Blanks:

1. For 80 square feet: \[ \text{Time for 80 sq ft} = 80 \times 0.4 = 32 \text{ minutes} \]

2. To find the unknown area (where time equals 40 minutes): \[ \text{Area} = \frac{40 \text{ min}}{0.4 \text{ min/sq ft}} = 100 \text{ sq ft} \]

Final Summary:

• Number of Square Feet:
  • 50 → 20 minutes
  • 80 → 32 minutes
  • 100 → 40 minutes
  • 160 → 64 minutes

Thus, the completed table is:

• For 80 square feet, the time is 32 minutes.
• For the area that takes 40 minutes, it is 100 square feet.