A river flows at 3 km/hr. A motor launch on this river covers 45 km downstream in exactly the time it takes to cover 27 km upstream. What is the speed of the launch in still water?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 12 km/hr
When two trips take the same time, the distances are in the same ratio as the speeds. Let the speed of the launch in still water be \(b\) km/hr.
Downstream speed \(=b+3\), upstream speed \(=b-3\)
\(\displaystyle \frac{b+3}{b-3}=\frac{45}{27}=\frac{5}{3}\)
\(3(b+3)=5(b-3)\), so \(3b+9=5b-15\)
\(2b=24\), so \(b=12\) km/hr
Check: \(45\div15=3\) hours and \(27\div9=3\) hours