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.
A. \(5 \mathrm{mph}\) B. \(10 \mathrm{mph}\) C. \(12 \mathrm{mph}\) D. \(20 \mathrm{mph}\)
Correct Answer: 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 \(x=5\)
