Question

The speed of a river current is 3 km/h A boat takes the same time to travel 15km upstream as it does to travel 18 km downstream . Find the speed of the boat in still water.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• The speed of a river current is 3 km/hr

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• A boat takes the same time to travel 15 km upstream as it does to travel 18 km downstream

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$\red{\underline \bold{To \: Find:}}$

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• Speed of the boat in still water.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the speed of boat in still river be 'x'

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

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$\purple\longrightarrow$ $\sf x - 3$

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

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$\purple\longrightarrow$ $\sf x + 3$

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$\red{\bold{We \: know \: that :}}$

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$\rm \dag \: \: Speed \: = \: \dfrac { Distance } { Time }$

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$\purple{\bold{Let \: time \: for \: downstream \: be \: 't1' </p><p>}}$

$\purple{\bold{Let \: time \: for \: upstream \: be \: 't2' }}$

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$\huge \sf For \: upstream$

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$\rm\dashrightarrow (x - 3) = \dfrac { 15 } { t1 }$

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$\bf\longmapsto t1 = \dfrac { 15 } { x - 3 }$

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$\huge \sf For \: downstream$

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$\rm\dashrightarrow (x + 3) = \dfrac { 18 } { t2 }$

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$\bf\longmapsto t2 = \dfrac { 18} { x + 3 }$

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$\purple{\bold{We \: know \: that \: t1\: = \: t2}}$

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$\sf \longmapsto \dfrac { 18 } { x + 3 } = \dfrac { 15 } { x - 3 }$

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$\sf \longmapsto 18x - 54 = 15x + 45$

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$\sf \longmapsto 18x - 15x = 45 + 54$

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$\sf \longmapsto 3x = 99$

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$\sf \longmapsto x = \dfrac { 99 } { 3 }$

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$\bf \dashrightarrow x = 33$

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Hence speed of boat in still water is 33 km/hr

$\rule{200}5$