Question

A motor boat whose speed is 18.km /hr in still water takes 1 hour more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

GivEn:

• Speed of boat in still water = 18 km/hr.

• It takes 1 hour more to go 24km upstream than to return downstream to the same spot.

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To find:

• Speed of stream.

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SoluTion:

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☯ Let speed of stream = s

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${\underline{\bf{\bigstar\; According\;to\: Question\;:}}}$

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Speed of boat in still water = 18 km/hr.

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★ Speed of boat upstream,

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$\dashrightarrow\sf Speed\;of\;water\;in\;still\:water - Speed\;of\;stream$

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$\dashrightarrow\bf 18 - s$

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★ Speed of boat down stream,

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$\dashrightarrow\sf Speed\;of\;water\;in\;still\:water + Speed\;of\;stream$

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$\dashrightarrow\bf 18 + s$

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Time taken for upstream = Time taken to cover downstream + 1

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$:\implies\sf \dfrac{Distance_{\;(upstream)}}{Speed_{\;(downstream)}} = \dfrac{Distance_{\;(downstream)}}{Speed_{\;(downstream)}} + 1$

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$:\implies\sf \dfrac{24}{18 - s} = \dfrac{24}{18 + s} + 1$

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$:\implies\sf \dfrac{24}{18 - s} = \dfrac{24 + (18 + s)}{18 + s}$

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$\;\;\;\;\;\;\small\sf \underline{Cross - multiplication\;:}$

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$:\implies\sf 24(18 + s) = 24(18 - s) + (18 - s)(18 + s)$

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$:\implies\sf 24(18 + s) = 24(18 - s) + (18)^2 - (s)^2\;\;\;\;\;\;\;\;\bigg\lgroup\bf (a + b)(a - b) = a^2 - b^2\bigg\rgroup$

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$:\implies\sf 24(18 + s) = 24(18 - s) + (18)^2 - (s)^2$

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$:\implies\sf 432 + 24s = 432 - 24s + 324 - s^2$

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$:\implies\sf \cancel{432} + 24s = \cancel{432} - 24s + 324 - s^2$

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$:\implies\sf 24s = - 24s + 324 - s^2$

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$:\implies\sf s^2 + 48s - 324 = 0$

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$\;\;\;\;\;\;\small\sf \underline{Splitting\;middle\;term\;:}$

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$:\implies\sf s^2 + 54s - 6s - 324 = 0$

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$:\implies\sf s(s + 54) - 6(s + 54) = 0$

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$:\implies\sf (s + 54)(s - 6) = 0$

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$:\implies\sf s = 6, - 54$

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$:\implies\sf s \neq - 54\;\;\;\;\;\;\;\;\bigg\lgroup\bf Speed\;of\;stream\: can't\;be\;negative.\bigg\rgroup$

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$:\implies{\underline{\boxed{\bf{\pink{s = 6\;km/hr}}}}}\;\bigstar$

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$\therefore$ Hence, Speed of stream is 6 km/hr.

Answer 2

HERE IS THE EASY METHOD FOR YOUR QUESTION.

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr

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