Question

21. Boat goes 30 km upstream and 44 km
downstream in 10 hrs. It goas 40 km upstream
and 55 km downstream In 13 hrs. Speed of
stream and boat in still water are
hr​

Answer 1

AnswEr :

Let the Speed of Boat in Still water be x Km/hr, and Speed of Stream be y Km/hr.

• Upstream = (x - y) Km/hr
• Downstream = (x + y) Km/hr

$\text{Let, \dfrac{1}{ \text{(x - y)}} = a \:\:and, \dfrac{1}{ \text{(x + y)}} = b}$

• According to the 1st Part of Question :

$\longrightarrow \tt \dfrac{Distance_1}{Upstream} + \dfrac{Distance_2}{Downstream} = 10 \:hrs \\ \\\longrightarrow \tt \dfrac{30}{(x - y)} + \dfrac{44}{(x + y)} = 10 \: hrs \\ \\\longrightarrow \tt30a + 44b = 10 \qquad \qquad \frac{ \quad}{} \:eq.(1)$

• According to the 2nd Part of Question :

$\longrightarrow \tt \dfrac{Distance_1}{Upstream} + \dfrac{Distance_2}{Downstream} = 13 \:hrs \\ \\\longrightarrow \tt \dfrac{40}{(x - y)} + \dfrac{55}{(x + y)} = 13 \: hrs \\ \\\longrightarrow \tt40a + 55b = 13 \qquad \qquad \frac{ \quad}{} \:eq.(2)$

$\rule{300}{1}$

• Multiplying eq.( 1 ) by 40 and, eq.( 2 ) by 30 and, Subtracting eq.( 2 )from ( 1 ) :

$\implies\tt \quad120a + 176b = 40 \\ \\\implies\tt - (120a + 165b = 39) \\ \frac{ \qquad \qquad \qquad \qquad \qquad\qquad}{} \\\implies\tt \quad11b = 1 \\ \\\implies \blue{\tt \quad b = \dfrac{1}{11}}$

• Putting the value of b in eq.( 1 ) :

$\Longrightarrow \tt30a + 44b = 10 \\ \\\Longrightarrow \tt30a + \cancel{44}\times \dfrac{1}{ \cancel{11}} = 10 \\ \\\Longrightarrow \tt30a + 4 = 10 \\ \\\Longrightarrow \tt30a = 10 - 4 \\ \\\Longrightarrow \tt30a = 6 \\ \\\Longrightarrow \tt a = \cancel\dfrac{6}{30} \\ \\\Longrightarrow \blue{\tt a = \dfrac{1}{5} }$

$\rule{300}{2}$

• Upstream = (x - y) = 5
• Downstream = (x + y) = 11

• we will solve this equation now :

↠ x – y = 5

↠ x + y = 11

$\rule{100}{1}$

↠ 2x = 16

• Dividing both term by 2

↠ x = 8 Km/hr⠀⠀⠀[ Speed of Boat ]

$\rule{150}{2}$

• Using the value of x in Downstream :

↠ x + y = 11

↠ 8 + y = 11

↠ y = 11 – 8

↠ y = 3 Km/hr ⠀⠀⠀[ Speed of Stream ]

⠀

∴ Therefore, Speed of Boat will be 8 Km/hr and, Speed of Stream will be 3 Km/hr.

#answerwithquality #BAL

Answer 2

$\huge{\underline {\underline {\mathfrak{Solution}}}}$

Let speed of boat is still water be x km/h and speed of steam be y km/h.

Speed upstream = (x-y) km/h

Speed downstream = (x+y) km/h

Let,

$\frac{1}{x - y} = a \: and \: \frac{1}{x + y} = b$

$\frac{30}{x - y} + \frac{44}{x + y} = 10 \\ = > 30a + 44b = 10 \\ = > 120a + 176b = 40</strong><strong>$

_________(i)

and

$\frac{40}{x - y} + \frac{55}{x + y} = 13 \\ = > 40a + 55b = 13 \\ = > 120a + 165b = 39</strong><strong>$

_________(ii)

On subtracting (ii) from (i), we get

$b = \frac{1}{11 }$

$\therefore \: 30a + 4 = 10 \\ = > 30a = 6 \\ = > a = \frac{1}{5} \\ \therefore \: x - y = 5 \: and \: x + y = 11$

On solving, we get,

$x = 8 \: and \: y = 3 \\ \therefore \: speed \: of \: boat \: in \: still \: water \: \\ = 8km</strong><strong>/</strong><strong>h</strong><strong>$

and speed of stream = 3km/h