Question

A motor boat, whose speed is 20 km/hr in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.​

Answer 1

Step-by-step explanation:

$\huge\mathfrak\orange{Question:-}$

A motor boat, whose speed is 20 km/hr in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot.

Find the speed of the stream.

$\huge\mathfrak\red{Answer:-}$

$\huge\mathbb\green{Solution⇛}$

$Let, \: the \: speed \: of \: the \: stream \: be \:  x \:  km/hr \\ Speed \: of \: boat \: in \: still \: water \:  = \: 20 \:  km/hr$

$∴ \: Speed \: of \: boat \: with \: downstream  \: 20+x \:  km/hr \\ ∴  \: Speed \: of \: boat \: with \: upstream \:  20−x  \: km/hr$

$As \: per \: given \: condition$

$\frac{48}{20 - x} - \frac{48}{20 + x} =1$

$⟹48 \: [ \frac{1}{20 - x} - \frac{1}{20 + x} ] \: = 1$

$⟹[ \frac{20 + x \: - \: 20 + x}{(20 - x) \: (20 + x)} ] \: = \frac{1}{48}$

$⟹ \: \frac{2x}{400 - x {}^{2} } = \frac{1}{48}$

$⟹\: 96x \: = \: 400 \: - x {}^{2}$

$⟹x {}^{2} +96x−400=0$

$⟹x {}^{2} +100x−4x−400$

$⟹ \: x(x+100)−4(x+100)=0$

$⟹ \: (x−4)(x+100)=0$

$Either,  \: x=4 or x=−100$

$⇝∵  \: Speed \: cannot \: be \: negative \: \\  ⇝∴ \: x=4  \: km/hr \: is \: considered.$

$\huge\mathbb\green{➽hence,  the \: speed \: of \: the \: stream \:  =4 \:  km/hr}$

Answer 2

$\huge\mathbb\fcolorbox{purple}{lavenderblush}{✰Answer}$

Let, the speed of the stream be x km/hr

Speed of boat in still water =20 km/hh

$\begin{gathered}∴ \: Speed \: of \: boat \: with \: downstream \: 20+x \: km/hr \\ ∴ \: Speed \: of \: boat \: with \: upstream \: 20−x \: km/hr\end{gathered}$

As per given condition

$\frac{48}{20 - x} - \frac{48}{20 + x} =1$

$⟹48 \: [ \frac{1}{20 - x} - \frac{1}{20 + x} ] \: = 1$

$⟹[ \frac{20 + x \: - \: 20 + x}{(20 - x) \: (20 + x)} ] \: = \frac{1}{48}$

$⟹ \: \frac{2x}{400 - x {}^{2} } = \frac{1}{48}$

$⟹\: 96x \: = \: 400 \: - x {}^{2}$

$⟹x {}^{2} +96x−400=0$

$⟹x {}^{2} +100x−4x−400$

$⟹ \: x(x+100)−4(x+100)=0⟹x(x+100)−4(x+100)=0$

$⟹ \: (x−4)(x+100)=0⟹(x−4)(x+100)=0$

Either, x=4 or x=−100

$\begin{gathered}⇝∵ \: Speed \: cannot \: be \: negative \: \\ ⇝∴ \: x=4 \: km/hr \: is \: considered.\end{gathered}$

$\huge\mathbb\green{➽hence, the \: speed \: of \: the \: stream \: =4 \: km/hr}$