The speed of a boat in still water is three times the speed of the stream. Over a 40 km stretch of the river, the boat takes 2 hours more to go upstream than to go downstream. What is the speed of the boat in still water?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15 km/hr
Write the stream’s speed as \(s\); the boat’s speed is then \(3s\), so both trip speeds are multiples of \(s\).
Upstream speed \(=3s-s=2s\), downstream speed \(=3s+s=4s\)
\(\displaystyle \frac{40}{2s}-\frac{40}{4s}=2\)
\(\displaystyle \frac{20}{s}-\frac{10}{s}=\frac{10}{s}=2\), so \(s=5\) km/hr
Speed of the boat in still water \(=3\times5=15\) km/hr
Check: \(40\div10=4\) hr upstream and \(40\div20=2\) hr downstream; the difference is 2 hr