The speed of a boat in still water is 18 km/h and the speed of the current is 6 km/h. In how much time (in hours) will the boat travel a distance of 90 km upstream and the same distance downstream?
Step 1 — Effective speeds:
Downstream \(= 18 + 6 = 24\) km/h; upstream \(= 18 - 6 = 12\) km/h.
Step 2 — Time for each leg:
\[T_{down} = \frac{90}{24} = \frac{15}{4}\ \text{h},\quad T_{up} = \frac{90}{12} = \frac{15}{2}\ \text{h}\]
Step 3 — Total time:
\[\frac{15}{4} + \frac{15}{2} = \frac{15 + 30}{4} = \frac{45}{4} = 11\tfrac{1}{4}\ \text{hours}\]
Therefore the total time is \(\mathbf{11\tfrac{1}{4}}\) hours.
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