The speed of a boat in still water is 12 km/h and the speed of the stream is \(x\) km/h. If in travelling 270 km upstream, the boat takes 66\(\tfrac{2}{3}\)% more time than travelling 270 km downstream, find the value of \(x\).

2 kmph
4 kmph
1 kmph
3 kmph

Correct answer: 3 kmph

Solution

If upstream time is 66\(\tfrac{2}{3}\)% more than downstream time, then upstream time is \(\frac{5}{3}\) times downstream time. For equal distances, time is inversely proportional to speed, so \(\frac{12+x}{12-x} = \frac{5}{3}\). Solving gives \(x = 3\) km/h.

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