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The distance between two points is 36 km. A boat rows in still water at 6 kmph. It takes 8 hours less to cover this distance in downstream in comparison to that in upstream. The rate of stream is
- A3 kmph
- B2 kmph
- C2.5 kmph
- D4 kmph
Answer not set
Discussion 1
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Solution
Let speed of stream = $x$ kmph
=> Speed of boat downstream = $(6 + x)$ kmph
Speed upstream = $(6 - x)$ kmph
Using, $time = \frac{distance}{speed}$
=> $\frac{36}{6 - x} - \frac{36}{6 + x} = 8$
=> $\frac{1}{6 - x} - \frac{1}{6 + x} = \frac{8}{36}$
=> $\frac{(6 + x) - (6 - x)}{(6 + x) (6 - x)} = \frac{2}{9}$
=> $\frac{2x}{36 - x^2} = \frac{2}{9}$
=> $\frac{x}{36 - x^2} = \frac{1}{9}$
=> $36 - x^2 = 9x$
=> $x^2 + 9x - 36 = 0$
=> $x^2 + 12x - 3x - 36 = 0$
=> $x (x + 12) - 3 (x + 12) = 0$
=> $x = 3 , -12$
$\because$ Speed cant be negative, => $x = 3$ kmph
Let speed of stream = $x$ kmph
=> Speed of boat downstream = $(6 + x)$ kmph
Speed upstream = $(6 - x)$ kmph
Using, $time = \frac{distance}{speed}$
=> $\frac{36}{6 - x} - \frac{36}{6 + x} = 8$
=> $\frac{1}{6 - x} - \frac{1}{6 + x} = \frac{8}{36}$
=> $\frac{(6 + x) - (6 - x)}{(6 + x) (6 - x)} = \frac{2}{9}$
=> $\frac{2x}{36 - x^2} = \frac{2}{9}$
=> $\frac{x}{36 - x^2} = \frac{1}{9}$
=> $36 - x^2 = 9x$
=> $x^2 + 9x - 36 = 0$
=> $x^2 + 12x - 3x - 36 = 0$
=> $x (x + 12) - 3 (x + 12) = 0$
=> $x = 3 , -12$
$\because$ Speed cant be negative, => $x = 3$ kmph