A river flows at a speed of 6 miles per hour. A boat travels 30 miles upstream and then returns downstream in a total time of 4.5 hours. The speed of the boat in still water ismiles per hour.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the ability to solve rational equations in a real-world context, specifically involving rates and proportions.
Key Concept Explanation
The problem involves setting up and solving a rational equation based on the given information about the boat's travel times and speeds.
Step-by-step Solution
1. Let be the speed of the boat in still water. The speed upstream is and downstream is .
2. The time taken upstream is and downstream is .
3. Total time equation: .
4. Find a common denominator: .
5. Multiply each term by the common denominator: .
6. Simplify and solve for :
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