A motor boat can travel at 10 km/hr in still water. It travelled 91 km downstream in a river and then returned to the starting point, taking altogether 20 hours. Find the rate of flow of the river?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 km/hr
The river adds its speed downstream and takes it away upstream. Let the speed of the river be \(x\) km/hr; the time down and the time back must together make 20 hours.
Downstream speed \(=10+x\), upstream speed \(=10-x\)
Total time, each part being distance ÷ speed: \(\displaystyle\frac{91}{10+x}+\frac{91}{10-x}=20\)
Over the common denominator \(100-x^{2}\), the numerator is \(91\times20\): \(\displaystyle\frac{91\times20}{100-x^{2}}=20\)
So \(100-x^{2}=91\), which gives \(x^{2}=9\) and a river speed of \(x=3\) km/hr
Shortcut:
Try the options: with 3 km/hr the boat goes downstream at 13 km/hr and upstream at 7 km/hr
\(91\div13=7\) hours and \(91\div7=13\) hours, which make 20 hours