3. The figure shows a straight portion of the course for a city marathon. The water station Wis located at the midpoint of AB. a. What is the length of the course from point A to point W? 70 meters b. Write a paragraph proof for your answer to part a. A (5x - 110) m W (2x + 100) m 19 B
3. The figure shows a straight portion of the course for a city marathon. The water station Wis located at the midpoint of AB. a. What is the length of the course from point A to point W? 70 meters b. Write a paragraph proof for your answer to part a. A (5x - 110) m W (2x + 100) m 19 B
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
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![**Course Length Calculation for City Marathon**
3. The figure shows a straight portion of the course for a city marathon. The water station \(W\) is located at the midpoint of \( \overline{AB} \).
a. **Question:** What is the length of the course from point \(A\) to point \(W\)?
**Answer:** 70 meters
b. **Question:** Write a paragraph proof for your answer to part a.
**Diagram Explanation:**
- The diagram illustrates a straight course section with points \(A\) and \(B\). The water station \(W\) is located at the midpoint of segment \( \overline{AB} \).
- The distance from \(A\) to \(W\) is labeled as \(5x - 110\) meters.
- The distance from \(W\) to \(B\) is labeled as \(2x + 100\) meters.
**Calculations:**
1. Two equations are written based on the distances:
\[
5x - 110 = 2x + 100
\]
2. Simplifying the equation:
\[
5x - 2x = 100 + 110
\]
\[
3x = 210
\]
\[
x = 70
\]
Thus, the length of the course from point \(A\) to \(W\) is 70 meters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12a1ba4a-9eea-484c-989f-6e04f409a1c7%2Fdf583f3a-6edc-4267-b63d-3803ba297779%2Foae4y39_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Course Length Calculation for City Marathon**
3. The figure shows a straight portion of the course for a city marathon. The water station \(W\) is located at the midpoint of \( \overline{AB} \).
a. **Question:** What is the length of the course from point \(A\) to point \(W\)?
**Answer:** 70 meters
b. **Question:** Write a paragraph proof for your answer to part a.
**Diagram Explanation:**
- The diagram illustrates a straight course section with points \(A\) and \(B\). The water station \(W\) is located at the midpoint of segment \( \overline{AB} \).
- The distance from \(A\) to \(W\) is labeled as \(5x - 110\) meters.
- The distance from \(W\) to \(B\) is labeled as \(2x + 100\) meters.
**Calculations:**
1. Two equations are written based on the distances:
\[
5x - 110 = 2x + 100
\]
2. Simplifying the equation:
\[
5x - 2x = 100 + 110
\]
\[
3x = 210
\]
\[
x = 70
\]
Thus, the length of the course from point \(A\) to \(W\) is 70 meters.
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