A man rows a boat at a speed of \(15 \mathrm{mph}\) in still water. Find the speed of the river if it takes her 4 hours 30 minutes to row a boat to a place 30 miles away and return.
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Correct Answer: Option C
Explanation:
Let the speed of the river \(=\mathrm{x} \mathrm{mph}\), then
Time taken row 30 miles upstream and 30 miles downstream \(=30 /(15-x)+30 /(15+x)=\) \(9 / 2\)
\(=10 /(15-x)+10 /(15+x)=3 / 2\)
\(=2[10(15+x)+10(15-x)]=3(15-x)^{2}\)
\(=300+20 x+300-20 x=675-3 x^{2}\)
\(x^{2}=25\) or \(x=5\)
Let the speed of the river \(=\mathrm{x} \mathrm{mph}\), then
Time taken row 30 miles upstream and 30 miles downstream \(=30 /(15-x)+30 /(15+x)=\) \(9 / 2\)
\(=10 /(15-x)+10 /(15+x)=3 / 2\)
\(=2[10(15+x)+10(15-x)]=3(15-x)^{2}\)
\(=300+20 x+300-20 x=675-3 x^{2}\)
\(x^{2}=25\) or \(x=5\)