Example: Finding Running and Biking Speeds Using a Known Total Distance
Apply the distance, rate, and time problem-solving strategy to find two unknown speeds for consecutive trip segments when their distances add up to a known total.
Problem: Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he rode his bike until 9:45. He covered a total distance of miles. His speed when biking was times his speed when running. Find Cruz's biking and running speeds.
- Read and draw: Sketch the situation with one path labeled "run" (from 6:00 to 7:30) and another labeled "bike" (from 7:30 to 9:45, times faster). The total distance is miles.
- Identify: The running speed and the biking speed.
- Name: Let = the running speed. The biking speed is . Calculate elapsed times: running from 6:00 to 7:30 is hours; biking from 7:30 to 9:45 is hours. Multiply rate by time to find distance expressions:
- Run: Rate = , Time = , Distance =
- Bike: Rate = , Time = , Distance =
- Translate: The sum of both distances equals the total distance:
- Solve: Simplify the terms: The running speed is miles per hour. The biking speed is miles per hour.
- Check: The running distance is miles. The biking distance is miles. The total distance is miles.
- Answer: Cruz's running speed is mph and his biking speed is mph.
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Example: Finding Running and Biking Speeds Using a Known Total Distance
Learn After
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