Question

a motor boat whose speed is 18km/hr in still water takes 1 hour more to go to 24km upstrem than to return downstrean to the same spot.fine the speed of the stream​

Answer 1

AnswEr :

6 km/hrs

$\bf{\Large{\green{\underline{\underline{\rm{Given\::}}}}}}$

A motor boat whose speed is 18km/hrs in still water takes 1 hour more to go to 24 km upstream than to return downstream to the same spot.

$\bf{\Large{\red{\underline{\underline{\bf{To\:Find\::}}}}}}$

The speed of the stream.

$\bf{\Large{\purple{\underline{\underline{\sf{Explanation\::}}}}}}$

Let the speed of the stream be R

Let $\sf{t_{1}}$ and $\sf{t_{2}}$ be the time for upstream and downstream.

$\bf{\large{\underline{\underline{\sf{First\:Case\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{A\:motor\:boat\:speed\:for\:upstream=\:(18-R)km/hr}\\ \sf{Distance\:=\:24km}\\ \sf{Time=t_{1}}\end{cases}}$

Formula use :

$\bf{\large{\boxed{\sf{Time\:=\:\frac{Distance}{Speed} }}}}}$

$\dashrightarrow\tt{t_{1}=\dfrac{24}{18-R} }$

$\bf{\large{\underline{\underline{\sf{Second\:Case\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{A\:motor\:boat\:speed\:for\:downstream=\:(18+R)km/hr}\\ \sf{Distance\:=\:24km}\\ \sf{Time=t_{2}}\end{cases}}$

$\dashrightarrow\tt{t_{2}=\dfrac{24}{18+R} }$

$\bf{\large{\red{\underline{\underline{\tt{A.T.Q\::}}}}}}$

$\longrightarrow\tt{t_{1}=t_{2}+1}\\\\\ \\ \longrightarrow\tt{\dfrac{24}{18-R} =\dfrac{24}{18+R} +1}\\\\\\\\\longrightarrow\tt{24(18+R)=24(18-R)+(18-R)(18+R)}\\\\\\\\\longrightarrow\tt{\cancel{432}+24R=\cancel{432}-24R+324\cancel{+18R}\cancel{-18R}-R^{2} }\\\\\\\\\longrightarrow\tt{24=-24R+324-R^{2} }\\\\\\\\\longrightarrow\tt{R^{2} +24R+24R-324=0}\\\\\\\\\longrightarrow\tt{R^{2} +48R-324=0}\\\\\\\\\longrightarrow\tt{R^{2} +54R-6R-324=0}$

$\longrightarrow\tt{R(R+54)-6(R+54)=0}\\\\\\\\\longrightarrow\tt{(R+54)(R-6)=0}\\\\\\\\\longrightarrow\tt{R+54=0\:\:\:\:\:\;Or\:\:\:\:\:\:\:R-6=0}\\\\\\\\\longrightarrow\tt{\red{R=-54}\:\:\:\:\:\:\:Or\:\:\:\:\:\:R=6}}$

∴ We know that negative value isn't acceptable.

So,

The speed of the stream R = 6 km /hrs.

Answer 2

Answer:

Step-by-step explanation:

Given :

        The speed of the motor bike instill water is 18 kmph,

        It takes 1 hour to travel upstream & return to same spot,.

From this information we can say that,

⇒ The speed of motor boat (boat's engine) = 18 kmph ,

⇒ It traveled 24 km upstream & 24km downstream in 1 hour,.

_____________________________________________________________

To Find :

The speed of stream .

_____________________________________________________________

We know that,

time =

So,

Let the speed of stream be x,

Then,

we can say that,

⇒   .....(i)      (All the units are in hour km per hour,etc,.)

⇒

⇒

⇒

⇒

⇒ -x² - 48x + 324 = 0

⇒ x² + 48x - 324 = 0

⇒ x² - 6x + 54x - 324 = 0

⇒ x (x -6) + 54(x - 6) = 0

⇒ (x + 54)(x - 6) = 0

For the equation to be 0,

Either,

⇒ x + 54 = 0 (or) x - 6 = 0

⇒ x = -54 (or) x = 6

⇒ x = 6 (As speed can't be negative, x ≠ -54)

     ∴ The speed of the stream is 6 kmph

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