A boat goes 30 km downstream from a jetty P to a jetty Q. Without stopping, it then turns back and goes 18 km upstream from Q to a jetty R. The whole journey takes 4 hours. The river flows at 3 km/hr. What is the speed of the boat in still water?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 12 km/hr
Each leg takes distance ÷ speed hours, and the two times add up to 4 hours. Let the speed of the boat in still water be \(b\) km/hr.
Downstream speed \(=b+3\), upstream speed \(=b-3\)
\(\displaystyle \frac{30}{b+3}+\frac{18}{b-3}=4\)
Multiplying by \((b+3)(b-3)\): \(30(b-3)+18(b+3)=4(b^{2}-9)\)
\(48b-36=4b^{2}-36\), so \(4b^{2}=48b\)
The speed is not 0, so \(b=12\) km/hr
Check: \(30\div15=2\) hours and \(18\div9=2\) hours; \(2+2=4\) hours