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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?
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A) 8 kms. |
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B) 12 kms. |
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C) 6 kms. |
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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
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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