Math Problem Statement
Determine whether the statement makes sense and explain your reasoning, I ran 2000 meters and you ran 2000 yards in the same time, so I ran at a faster rate
Solution
The statement makes sense. Here's why:
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Meters vs. Yards: 1 meter is approximately 1.09361 yards. Therefore, 2000 meters is longer than 2000 yards.
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Conversion: If you convert 2000 meters to yards, it would be: So, 2000 meters is approximately 2187.22 yards, which is longer than 2000 yards.
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Speed Comparison: Since you ran a longer distance (2187.22 yards) compared to the other person who ran 2000 yards in the same amount of time, you must have been running at a faster rate to cover the greater distance.
Thus, the statement is correct: you ran at a faster rate because you covered a greater distance (2000 meters vs. 2000 yards) in the same amount of time.
Do you have any questions, or would you like further details?
Here are 5 related questions for deeper understanding:
- How would you calculate the rate of running if the time taken was 10 minutes?
- How do you convert meters per second to miles per hour?
- What is the ratio of the distances between meters and yards?
- How much time would you save if you ran the same distance at the same rate but for 1600 meters?
- How does converting units affect speed calculations in other sports like swimming?
Tip: Always ensure unit consistency when comparing distances or speeds across different measurement systems.
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Math Problem Analysis
Mathematical Concepts
Unit Conversion
Speed and Rate
Distance
Formulas
1 meter = 1.09361 yards
Rate = Distance / Time
Theorems
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Suitable Grade Level
Grades 6-8