A man can row a boat in still water at the rate of 6 km per hour. If the stream flows at the rate of 2 km/hour, it takes half the time going downstream than going upstream the same distance. His average speed for an upstream and downstream trip is:

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6 km / hour

\frac{16}{3} km / hour

Insufficient data to arrive at the answer

None of the above

answer is B.

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Detailed Solution

Given, the boat speed is

6 km / hr

And stream of speed is

2 km / hr

.
Suppose the distance travelled upstream and downstream be separated by x kilometers.
So, boat relative speed when moving upstream,

= (6 - 2) = 4 km / hr .

Boat relative speed when moving downstream,

= (6 + 2) = 8 km / hr

Time spent moving upstream,

t = \frac{distance}{speed}

t = \frac{x}{4} hr

Time spent moving downstream,

t = \frac{x}{8} hr

Overall time which is taken by boat,

= \frac{x}{4} + \frac{x}{8}

= \frac{3 x}{8} hr

Now we know that,
Average speed

= \frac{Total distance covered}{Total time taken}

v = \frac{2 xkm}{\frac{3 x}{8} hr}

v = \frac{2 x}{3 x} \times \frac{8 km}{hr}

v = \frac{16}{3} km / hr

Thus, the average speed for an upstream and downstream trip is 16/3 km/hr.
Option 2 is correct.

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