Question

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

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Speed of moter boat in still water is 18 km/hr

• While going with upstream takes 1 hr more then going with downstream for the same 24 km

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• The speed of stream

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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• Let the speed of stream be 's'

• Let the time taken in stream be 'T1'

• Let the time taken in downstream be 'T2'

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$\underline{\bold{\texttt{Speed in upstream :}}}$

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➠ 18 - s

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$\underline{\bold{\texttt{Showed in downstream :}}}$

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➠ 18 + s

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We know that ,

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$\bf \boxed { Time = \dfrac { Distance } { Speed } }$ ⚊⚊⚊⚊ ⓵

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For upstream

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• Time = T1

• Distance = 24 km

• Speed = 18 - s

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⟮ Putting the values in ⓵ ⟯

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: : ➜ $\bf Time = \dfrac { Distance } { Speed }$

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: ➜ $\bf T1 = \dfrac { 24 } { 18 - s }$ ⚊⚊⚊⚊ ⓶

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For downstream

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• Time = T2

• Distance = 24 km

• Speed = 18 + s

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⟮ Putting the values in ⓵ ⟯

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: : ➜ $\bf Time = \dfrac { Distance } { Speed }$

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: ➜ $\bf T2 = \dfrac { 24 } { 18 + s }$ ⚊⚊⚊⚊ ⓷

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Given that ,time taken in upstream is 1 hour more than time taken in downstream for 24 km

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Thus,

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: ➜ T1 = T2 + 1

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From ⓶ & ⓷

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: ➜ $\sf \bigg\lgroup\dfrac { 24 } { 18 - s }\bigg\rgroup = \bigg\lgroup\dfrac { 24 } { 18 + s }+ 1\bigg\rgroup$

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: ➜ $\sf \bigg\lgroup\dfrac { 24 } { 18 - s }\bigg\rgroup = \bigg\lgroup\dfrac { 24 + 18 + s} { 18 + s }\bigg\rgroup$

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: ➜ $\sf \bigg\lgroup\dfrac { 24 } { 18 - s } \bigg\rgroup= \bigg\lgroup\dfrac { 42 + s} { 18 + s }\bigg\rgroup$

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: ➜ (42 + s)(18 - s) = 24(18 + s)

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: ➜ 756 - 42s + 18s - s² = 432 + 24s

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: ➜ s² + 24s + 42s - 18s - 756 + 432 = 0

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: ➜ s² + 48s - 324 = 0

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: ➜ s² + 54s - 6s - 324 = 0

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: ➜ s(s + 54) -6(s + 54) = 0

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: ➜ (s + 54)(s - 6) = 0

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• s = - 54
• s = 6

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As speed can't be negative

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Thus ,

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: : ➨ s = 6 km/hr

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• Hence the speed of stream is 6 km/hr

Answer 2

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