A boat takes 6 hours to travel from place M to N downstream and back from N to M upstream. If the speed of the boat in still water is 4 km./hr., what is the distance between the two places?

A) 8 kms.

B) 12 kms.

C) 6 kms.

D) Data inadequate

Correct answer:
D) Data inadequate

Description for Correct answer:
Total time = 6 hours.

Speed of the boat in still water = 4 km/hr.

Let the distance between M and N be D, and the speed of the stream be x.

\( \Large D[\frac{1}{4 + x} + \frac{1}{4 - x} ] = 6 \)

\( \Large D[\frac{4 - x + 4 + x}{(x + x) (4 - x)} ] = 6 \)

\( \Large D [\frac{8}{4^{2} - x^{2}}] = 6 \)

\( \Large \frac{8D}{16 - x^{2}} = 6 \)

\( \Large D = \frac{6}{8} (16 - x^{2}) = \frac{3}{4}(16 - x^{2}) \)

Since the speed of the stream (x) is not given, the distance D cannot be determined


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