Question

(D) A man travels in a boat 36 km down stream of a river and the same distance up stream of this river in
a total time of 9 hours. If the speed of his boat in still water is 12 km/hr, find the speed of the river
current. [Take V3 = 1.7]​

Answer 1

GIVEN :-

• Total distance travelled = 36 km

• Total time taken = 9 hours

• Speed of boat in still water = 12 km/hr

TO FIND :-

• Speed of the river

SOLUTION :-

Let the speed of river be x.

Speed of boat downstream = ( 12 + x ) km/hr

Speed of boat upstream = ( 12 - x ) km/hr

$\bf Time \ taken = \dfrac{Distance}{Speed}$

Time taken to travel downstream = $\sf\dfrac{36}{(x+2)}$  hours

Time taken to travel upstream = $\sf\dfrac{36}{(x-2)}$ hours

 According to the question,

 $\longrightarrow\quad \sf \dfrac{36}{12+x}+\dfrac{36}{12-x}= 9 \\\\\longrightarrow\quad\dfrac{36(12+x)+36(12-x)}{(12+x)(12-x)}=9 \\\\\longrightarrow\quad\dfrac{36(12+x+12-x)}{(12^2-x^2)}} = 9 \\\\\longrightarrow\quad36 \times 24 = 9 (144-x^2)\\\\\longrightarrow\quad144-x^2 = \dfrac{36\times 24}{9}\\\\\longrightarrow\quad 144-x^2 = 96 \\\\\longrightarrow\quad x^2= 144-96 \\\\\longrightarrow\quad x^2 = 48 \\\\\longrightarrow\quad x = \sqrt{48} \\\\\longrightarrow\quad x = \sqrt{16\times 3}$

$\longrightarrow\quad \sf x = 4\sqrt{3} \\\\\longrightarrow\quad \sf x = 4\times 1.7 \\\\\longrightarrow\quad \bf x= 6.8$

           

Speed of the river = 6.8 km/hr

Answer 2

Answer:

$\tt {\pink{We \: have}}\begin{cases} \sf{\green{Total \: distance \: travelled = 36 \: km}}\\ \sf{\blue{Total \: time \: taken = 9 \: hours}}\\ \sf{\orange{Speed \: of \: boat \: in \: still \: water = 12 \: km/hr}}\\ \sf{\gray{Speed \: of \: the \: river \: current= \: ?}}\end{cases}$

• Let the speed of river current be x km/hr

Here, x < 12

Therefore,

• The speed of boat down the current = (12 + x) km/hr.

• The speed of boat up the current = (12 - x) km/hr.

_______________

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies \sf \dfrac{36}{12 + x} + \dfrac{36}{12 - x} = 9$

$:\implies \sf 36 \: (12 - x + 12 + x) = 9 \: (12 + x) \: (12 - x)$

$:\implies \sf 36 \times 24 = 9 \: (144 - {x}^{2} )$

$:\implies \sf 864 = 9 \: (144 - {x}^{2} )$

$:\implies \sf \dfrac{864}{9} = 144 - {x}^{2}$

$:\implies \sf 96 = 144 - {x}^{2}$

$:\implies \sf {x}^{2} = 144 - 96$

$:\implies \sf {x}^{2} = 48$

$:\implies \sf x= \sqrt{48}$

$:\implies \sf x= \sqrt{16 \times 3}$

$:\implies \sf x= \sqrt{4 \times 4 \times 3}$

$:\implies \sf x= 4\sqrt{3}$

$:\implies \sf x= 4 \times 1.7 \: \: \: \: \: \: \Bigg\lgroup \bf{Taking \: \sqrt{3} = 1.7 }\Bigg\rgroup$

$:\implies\underline{ \boxed{\textsf{\textbf{x = 6.8 km/hr}}}}$

$\therefore\underline{\textsf{ The speed of river current is \textbf{6.8 km/hr}}}.$