Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Question:**
A paint machine stripes an area of 20 sq mm per second. How many square meters will this machine paint in 8 hours?
**Solution Explanation:**
To solve this problem, we need to convert the painting rate from square millimeters to square meters and calculate the total area painted in 8 hours.
1. **Conversion Factors:**
- \(1 \text{ meter} = 1000 \text{ millimeters}\)
- Therefore, \(1 \text{ sq meter} = (1000 \text{ mm}) \times (1000 \text{ mm}) = 1,000,000 \text{ sq mm}\)
2. **Conversion of Rate:**
- The machine paints \(20 \text{ sq mm/sec}\).
- To convert this to square meters, divide by \(1,000,000\):
\[
\frac{20 \text{ sq mm}}{1,000,000} = 0.00002 \text{ sq meters/sec}
\]
3. **Total Time in Seconds:**
- 8 hours = \(8 \times 60 \times 60 = 28,800\) seconds
4. **Total Area Painted:**
- Multiply the rate by the time:
\[
0.00002 \text{ sq meters/sec} \times 28,800 \text{ sec} = 0.576 \text{ sq meters}
\]
**Answer:**
The machine will paint a total of 0.576 square meters in 8 hours.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1815343-0e1e-45bc-b31a-0935809f9211%2Fc970a1b8-3f46-4410-8b7f-c37cdee69878%2F0zmsmv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
A paint machine stripes an area of 20 sq mm per second. How many square meters will this machine paint in 8 hours?
**Solution Explanation:**
To solve this problem, we need to convert the painting rate from square millimeters to square meters and calculate the total area painted in 8 hours.
1. **Conversion Factors:**
- \(1 \text{ meter} = 1000 \text{ millimeters}\)
- Therefore, \(1 \text{ sq meter} = (1000 \text{ mm}) \times (1000 \text{ mm}) = 1,000,000 \text{ sq mm}\)
2. **Conversion of Rate:**
- The machine paints \(20 \text{ sq mm/sec}\).
- To convert this to square meters, divide by \(1,000,000\):
\[
\frac{20 \text{ sq mm}}{1,000,000} = 0.00002 \text{ sq meters/sec}
\]
3. **Total Time in Seconds:**
- 8 hours = \(8 \times 60 \times 60 = 28,800\) seconds
4. **Total Area Painted:**
- Multiply the rate by the time:
\[
0.00002 \text{ sq meters/sec} \times 28,800 \text{ sec} = 0.576 \text{ sq meters}
\]
**Answer:**
The machine will paint a total of 0.576 square meters in 8 hours.
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