Viral swims for 13 hours while going 24 km downstream and 36 km upstream. But he takes 12 hours to swim 36 km downstream and 24 km upstream. At what rate is the river flowing?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 km/hr
Let Viral’s speed in still water be \(b\) and the river’s speed \(s\) km/hr; downstream his speed is \(b+s\), upstream \(b-s\). Writing \(u=\frac{1}{b+s}\) and \(v=\frac{1}{b-s}\) turns each trip into a simple linear equation (time = distance × \(u\) or \(v\)).
The two trips:
\(24u+36v=13\) (1)
\(36u+24v=12\) (2)
Solving (adding and subtracting (1) and (2)):
Adding: \(60(u+v)=25\), so \(\displaystyle u+v=\frac{5}{12}\)
(1) − (2): \(12(v-u)=1\), so \(\displaystyle v-u=\frac{1}{12}\)
\(\displaystyle v=\frac{1}{4}\) and \(\displaystyle u=\frac{1}{6}\)
The speeds:
\(b+s=6\) and \(b-s=4\)
\(b=5\) km/hr, and the river flows at \(s=1\) km/hr