Question
7-50. Lydia drew a graph of four athletes in the final part of the triathlon, the 10 km run. She found the slope of each runner's line. Her results are listed below. Homework Help in Runner A: slope \( =\frac{2}{6} \) Runner B: slope \( =\frac{3}{7} \) Runner C : slope \( =\frac{5}{12} \) Runner D: slope \( =\frac{4}{10} \) \( \begin{array}{l}\text { List the runners from slowest to fastest. }\end{array} \)
Ask by Murray Donnelly. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Runner A is the slowest, followed by Runner D, then Runner C, and Runner B is the fastest.
Solution
1. Calculate each runner's slope (speed):
- Runner A: \( \frac{2}{6} = \frac{1}{3} \approx 0.333 \)
- Runner B: \( \frac{3}{7} \approx 0.429 \)
- Runner C: \( \frac{5}{12} \approx 0.417 \)
- Runner D: \( \frac{4}{10} = 0.4 \)
2. List the runners from slowest to fastest (from the smallest to the largest slope):
- Slowest: Runner A (\( \approx 0.333 \))
- Next: Runner D (\( 0.4 \))
- Next: Runner C (\( \approx 0.417 \))
- Fastest: Runner B (\( \approx 0.429 \))
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Simplify this solution The Deep Dive
To determine the order from slowest to fastest runner, we should first convert the slopes into decimals to make comparisons easier. - Runner A: \( \frac{2}{6} = 0.33 \) - Runner B: \( \frac{3}{7} \approx 0.43 \) - Runner C: \( \frac{5}{12} \approx 0.42 \) - Runner D: \( \frac{4}{10} = 0.40 \) Now we can arrange them from slowest to fastest based on their slopes (lower slope indicates slower pace): 1. Runner A: 0.33 2. Runner D: 0.40 3. Runner C: 0.42 4. Runner B: 0.43 In conclusion, the order from slowest to fastest is: Runner A, Runner D, Runner C, Runner B.
