Question

A motorboat whose speed is 15 kilometre per hour in still water goes 30 kilometre downstream and come back in a total time is of 4 hour 30 minutes find the speed of stream​

Answer 1

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

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• Speed of motorboat in still water is 30 km/hr

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• Distance = 30 km

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• Total time taken = 4 hours 30 minutes

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Speed of stream

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

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• Let the speed of stream be "x"

• Let time taken in downstream be t1

• Let time taken in upstream be t2

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

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➜ 15 + x

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

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➜ 15 - x

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$\underline{\bold{\texttt{We know that :}}}$

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➠ $\sf Time = \dfrac { Distance } { Speed }$

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$\underline{\bold{\texttt{Time taken while going downstream :}}}$

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➜ $\sf t1 = \dfrac { 30} { 15 + x}$

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$\underline{\bold{\texttt{Time taken while going upstream :}}}$

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➜ $\sf t2 = \dfrac { 30 } { 15 - x }$

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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➜ t1 + t2 = 4 hours 30 minutes

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⟮ 4 hours 30 minutes = $\sf 4 \dfrac { 1 } { 2 }$ ⟯

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➜ $\sf t1 + t2 = 4 \dfrac { 1 } { 2 }$

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➜ $\sf \dfrac { 30} { 15 + x} + \dfrac { 30 } { 15 - x } = 4 \dfrac { 1 } { 2 }$

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➜ $\sf \dfrac { 30(15 - x) + 30(15 + x) } { (15 + x)(15 - x) } = 4 \dfrac { 1 } { 2 }$

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➜ $\sf \dfrac { 450 - 30x + 450 + 30x } {15 ^2 - x ^2 } = 4 \dfrac { 1 } { 2 }$

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➜ $\sf \dfrac { 450 + 450 } {225 - x ^2 } = 4 \dfrac { 1 } { 2 }$

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➜ $\sf \dfrac { 900} {225 - x ^2 } = \dfrac { 9} { 2 }$

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Multiplying LHS & RHS by 9

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➜ $\sf \dfrac { 100} {225 - x ^2 } = \dfrac { 1} { 2 }$

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By cross multiplication

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➜ $\sf 200 = 225 - x ^2$

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➜ $\sf x ^2 = 225 - 200$

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➜ $\sf x ^2 = 25$

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➜ $\sf x = \sqrt {25}$

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➨ $\sf x = - 5 \:\:\:\:\:\:$ | $\:\:\:\:\:\:$x = 5

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As speed can't be negative hence x = 5

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• Therefore speed of stream is 5 km/hr

Answer 2

Given :-

• A motorboat whose speed is 15 kilometre per hour in still water goes 30 kilometre downstream and come back in a total time is of 4 hour 30 minutes.

To Find :-

• The speed of the stream = ?

Answer :-

• The speed of the stream = 5 km/hr

Explaination :-

▣ Let Speed of stream be x km/hr

▦ Speed of boat in downstream = (15 + x) km/hr

▩ Speed of boat in upstream = (15 - x) km/hr

❍ According to Question :-

→ 30/(15 + x) + 30/(15 - x) = 4 ½

→ 30/(15 + x) + 30/(15 - x) = 9/2

→ 30(15 - x) + 30(15 + x)/(15 + x) (15 - x) = 9/2

→ 450 - 30x + 450 + 30x/225 - x² = 9/2

→ 900/225 - x² = 9/2

→ 100/225 - x² = 2

→ 225 - x² = 2 × 100

→ 225 - x² = 200

→ 225 - 200 = x²

→ 25 = x²

→ x = 5 km/hr

Therefore,The speed of the stream is 5 km/hr.