When the river flows at 2 km/hr, a boat takes 10 hours to go 48 km downstream and come back to the starting point. The speed of the boat in still water stays the same. How long will the same round trip take on a day when the river flows at 5 km/hr?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12 hours 48 minutes
The first day’s trip gives the boat’s speed in still water. A faster river helps one leg but slows the other more, so the round trip takes longer on the second day.
Let the speed of the boat in still water be \(b\) km/hr
\(\displaystyle \frac{48}{b+2}+\frac{48}{b-2}=10\)
\(\displaystyle \frac{96b}{b^{2}-4}=10\), so \(10b^{2}-96b-40=0\), that is \(5b^{2}-48b-20=0\)
\((b-10)(5b+2)=0\); a speed is positive, so \(b=10\) km/hr
Check: \(48\div12=4\) hr and \(48\div8=6\) hr; \(4+6=10\) hr
With the river at 5 km/hr: downstream \(=15\) km/hr, upstream \(=5\) km/hr
Time \(\displaystyle =\frac{48}{15}+\frac{48}{5}=3.2+9.6=12.8\) hours
\(0.8\) hour \(=0.8\times60=48\) minutes, so the trip takes 12 hours 48 minutes