Solving a Uniform Motion Application: Boat Speed with Equal Travel Times
Apply the distance, rate, and time problem-solving strategy to find an unknown boat speed when different distances are covered in equal time—one segment upstream and one downstream.
Problem: On a river that flows at miles per hour, Danica can take a motorboat miles upstream in the same amount of time she can take her motorboat miles downstream. How fast is Danica's boat in a lake?
- Read and draw: Sketch the river paths — miles upstream and miles downstream. Create a rate–time–distance table.
- Identify: The boat's speed in still water (a lake).
- Name: Let = the boat's speed in still water. The upstream rate is ; the downstream rate is . Because , the times are and .
- Translate: The travel times are equal:
- Solve: Multiply both sides by the LCD, :
- Check: Upstream time: hour. Downstream time: hour. The times are equal.
- Answer: Danica's boat speed in a lake is mph.
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Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
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