Solving a Uniform Motion Application: Driving Rates on Different Roads
Apply the distance, rate, and time problem-solving strategy to find unknown speeds when a trip is divided into segments with a known total time.
Problem: Joon drove hours to his home, driving miles on the interstate and miles on country roads. If he drove mph faster on the interstate than on the country roads, what was his rate on the country roads?
- Read and draw: Sketch the two segments of the trip: miles on the interstate and miles on country roads. Create a rate-time-distance table.
- Identify: Joon's driving rate on the country roads.
- Name: Let = Joon's rate on country roads. His interstate rate is . The time spent on the interstate is and the time spent on country roads is .
- Translate: The total driving time is hours, meaning the sum of the times is :
- Solve: Multiply both sides by the least common denominator, : Divide by : The solutions are and . Speed cannot be negative, so mph.
- Check: Interstate time: hours. Country road time: hours. Total time: hours.
- Answer: Joon's rate on the country roads was mph.
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Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
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Learn After
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