Question

Mindy:

Cleans 3 rooms in 1.8 hours, and cleans 10 rooms in 6 hours.



Michael:

y = 0.75x

x = rooms cleaned

y = time spent

Mindy and Michael work at a hotel cleaning rooms. Review the data shown above. Which statement below is true?
Responses



A Mindy cleans rooms at a faster rate than Michael.Mindy cleans rooms at a faster rate than Michael.
B Mindy and Michael clean rooms at the same rate.Mindy and Michael clean rooms at the same rate.
C Michael cleans rooms at a faster rate than Mindy.Michael cleans rooms at a faster rate than Mindy.
D Not enough information is given to determine who cleans faster.

Answer 1

To determine who cleans faster, we need to calculate the cleaning rates for Mindy and Michael.

**Mindy's Cleaning Rate:**
1. From the information provided, we have two scenarios for Mindy:
- Cleans 3 rooms in 1.8 hours:
\[
\text{Rate} = \frac{3 \text{ rooms}}{1.8 \text{ hours}} = \frac{3}{1.8} \approx 1.67 \text{ rooms per hour}
\]
- Cleans 10 rooms in 6 hours:
\[
\text{Rate} = \frac{10 \text{ rooms}}{6 \text{ hours}} = \frac{10}{6} \approx 1.67 \text{ rooms per hour}
\]
- Mindy’s average rate is approximately 1.67 rooms per hour.

**Michael's Cleaning Rate:**
2. The equation for Michael is given as \( y = 0.75x \), where \( x \) is the number of rooms cleaned, and \( y \) is the time spent. To find his rate, we need to rearrange this equation. Time spent can be expressed as:
\[
y = 0.75x \implies \text{Time (hours)} = 0.75 \times \text{Rooms}
\]
- To find the rate (rooms per hour), we can calculate:
\[
\text{Rate} = \frac{x \text{ rooms}}{0.75x \text{ hours}} = \frac{1}{0.75} \approx 1.33 \text{ rooms per hour}
\]

**Comparison:**
- Mindy cleans at a rate of approximately 1.67 rooms per hour.
- Michael cleans at a rate of approximately 1.33 rooms per hour.

Based on these calculations, Mindy cleans rooms at a faster rate than Michael.

**Conclusion:**
The correct statement is:
A. Mindy cleans rooms at a faster rate than Michael.