Try It 7.97: Solving a Uniform Motion Application for Biking and Bus Speeds
Apply the distance, rate, and time problem-solving strategy to find unknown speeds when different modes of transportation are used and a time difference is known.
Problem: Kayla rode her bike miles home from college one weekend and then rode the bus back to college. It took her hours less to ride back to college on the bus than it took her to ride home on her bike, and the average speed of the bus was miles per hour faster than Kayla’s biking speed. Find Kayla’s biking speed.
- Read and draw: Sketch the journey with miles by bike and miles by bus. Create a rate-time-distance table.
- Identify: Kayla's biking speed.
- Name: Let = biking speed in mph. The bus speed is . The distance for both trips is miles. Because , the biking time is and the bus time is .
| Rate (mph) | Time (hrs) | Distance (miles) | |
|---|---|---|---|
| Bike | |||
| Bus |
- Translate: The bus ride took hours less than the bike ride, so the biking time minus equals the bus time:
- Solve: Multiply both sides by the least common denominator, : Divide by : Factor the trinomial: The solutions are and . Since speed cannot be negative, discard . Therefore, mph.
- Check: Biking time: hours. Bus time: hours. The bus ride was hours shorter.
- Answer: Kayla's biking speed was mph.
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Related
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Learn After
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