Question

a Boat goes some distance in upstream in 6 hours and covers the same distance in downstream in 4 hours if the speed of stream is 3 km per hour then the distance is

Answer 1

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Answer 2

Given

• A boat goes same distance towards upstream in 6 hrs. .

• And covered the same distance towards downstream in 4 hrs. .

$The \: speed \: of \: the \: stream \: is \: 3 km/hr .</p><p>\begin{gathered}\\\end{gathered} </p><p>$

$\begin{gathered}\huge\bf{\underbrace{\gray{TO\:FIND:-}}} \\\end{gathered}$

• The total distance covered by boat .

$\begin{gathered}\huge\bf{\underbrace{\gray{SOLUTION:-}}} \\ \\\end{gathered} </p><p>$

Let,

$\bf\red{Total\:distance}= X m \\ </p><p>\bf\red{Speed\:of\:boat} = U km/hr .$

Speed towards upstream :-

• Speed of boat - Speed of stream

$\begin{gathered}\bf\pink{:\implies\:(U\:-\:3)\:km/hr\:} \\ \\\end{gathered}$

Speed towards downstream :-

• Speed of boat + Speed of stream

$\begin{gathered}\bf\pink{:\implies\:(U\:+\:3)\:km/hr\:} \\ \\\end{gathered}$

:

Time towards upstream :-

$\\\checkmark✓ \begin{gathered}\bf\purple{Time\:=\:\dfrac{X}{U\:-\:3}\:hrs\:} \\ \\\end{gathered}$

$\begin{gathered}\rm{:\implies\:6\:=\:\:\dfrac{X}{U\:-\:3}\:} \\ \\\end{gathered}$

$\begin{gathered}\rm{:\implies\:6\:=\:\:\dfrac{X}{U\:-\:3}\:} \\ \\\end{gathered}$

$\begin{gathered}\bf{:\implies\:X\:=\:(U\:-\:3)\times{6}\:} \\ \\\end{gathered}$

Time towards downstream :-

$\huge\red\checkmark✓ \begin{gathered}\bf\purple{Time\:=\:\dfrac{X}{U\:+\:3}\:hrs\:} \\ \\\end{gathered}$

$\begin{gathered}\rm{:\implies\:4\:=\:\:\dfrac{X}{U\:+\:3}\:} \\ \\\end{gathered}$

$\begin{gathered}\bf{:\implies\:X\:=\:(U\:+\:3)\times{4}\:} \\ \\\end{gathered}$

☞︎︎︎ It is given that,

• The boat goes same distance both towards upstream and downstream .

$\begin{gathered}\bf\blue{:\implies\:\:(U\:-\:3)\times{6}\:=\:\:(U\:+\:3)\times{4}\:} \\\end{gathered}$

➳ 6U - 18 = 4U + 12

➳ 6U - 4U = 12 + 18

➳ 2U = 30

➳ U = 30/3

➳ U = 15 km/hr

$\large\therefore∴ Speed \: of \: the \: boat \: is \: "15 km/hr" .$

☯︎ Now, we can find the distance either from equation (1) or from the equation (2) . So, now we can put the value in equation (1),

$\begin{gathered}\blue\bigstar\:\bf\orange{Distance\:(X)\:=\:(U\:-\:3)\times{6}\:} \\ \\\end{gathered} \\ </p><p></p><p> </p><p> </p><p></p><p>\begin{gathered}\rm{:\implies\:Distance\:(X)\:=\:(15\:-\:3)\times{6}\:} \\ \\\end{gathered} \\ </p><p>:</p><p> </p><p> </p><p></p><p>\begin{gathered}\rm{:\implies\:Distance\:(X)\:=\:12\times{6}\:} \\ \\\end{gathered} \\ </p><p>:</p><p>$

$\begin{gathered}\bf\green{:\implies\:Distance\:(X)\:=\:72\:km\:} \\ \\\end{gathered}$

:

$\huge\red\therefore∴ The \: total \: distance \: is \: "72 km" .$