A motor boat can travel at 15 km/hr in still water. It traveled 63 km downstream in a river and then returned taking altogether 10 hr. What is the rate of flow of the river?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6 km/hr
Going downstream, the river’s flow adds to the boat’s speed; coming back upstream, it takes away from it. Let the speed of the river be \(x\) km/hr; the time for each leg is distance ÷ speed, and the two times add up to 10 hours.
Downstream speed \(=15+x\), upstream speed \(=15-x\)
\(\displaystyle \frac{63}{15+x}+\frac{63}{15-x}=10\)
\(\displaystyle \frac{63\times30}{225-x^2}=10\)
\(1890=2250-10x^2\)
\(x^2=36\), so \(x=6\) km/hr
Shortcut: Try the options in the time equation.
With 6 km/hr: downstream \(63\div21=3\) h and upstream \(63\div9=7\) h
\(3+7=10\) h, as given, so the speed of the river is 6 km/hr