Question

A steamer goes downstream from one
station to another in 9 hours. It covers the same
distance upstream in 10 hours. If the speed of the
stream is 1 km/h, find the speed of the steamer.​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• A steamer goes downstream from one station to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream is 1 km/h, find the speed of the steamer.

$\large\underline{ \underline{ \sf \maltese{ \:Given:- }}}$

Let the speed of the steamer be x km/h

• Speed of stream = $\sf\green{ 1km/h \:}$
• Then speed downstream = $\sf\green{ (x+1) \: km/h}$
• Speed upstream = $\sf\green{(x-1)\: km/h}$
• Speed of Steamer = ?

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: Distance \: = \: Speed \: × \: Time}} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\:\: to \:\:the\:\: Question :}} \\\end{gathered}\end{gathered}$

$\boxed{ \sf \red{ Distance \: Downstream \: = \: Distance \: Upstream }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 9( \: x\: + \: 1 \: ) \: = \:10( \: x \: - \: 1) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 9 x\: + \: 9 \: = \:10 x \: - \: 10 }}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ 9 x\: - \: 10x \: = \: - 10 \: - \: 9 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \cancel - x \: = \: \cancel - 19 }}$

$\qquad\quad {:} \longrightarrow \underline {\boxed{\sf{x = 19 }}}$

$\begin{gathered}\qquad \therefore\: \sf{ Speed \:of \: Steamer= \underline {\underline{19km/h }}}\\\end{gathered}$

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