Question

A motor boat whose speed is 18km/h in still water takes 1 hour more to go 24km up stream than to
return down stream to the same spot . Find the speed of the stream​

Answer 1

AnsWer :

6 km/h.

Given :

• A motor boat move upstream and downstream in water to the same spots.
• D = S.t.

To find :

The Speed of the Stream.

Solution :

Let the speed be x km/ h.

• Speed of boat in upstream be ( 18 - x )
• Speed of boat in Downstream be ( 18 + x )
• Total distance be 24 km, which is fixed.

Time taken to go, Upstream.

$\tt D_{istance} = S_{peed} \times t_{ime}.$

$\tt \dashrightarrow \frac{d}{s} = \frac{24}{18 - x}$

And, Time taken to go, Downstream.

$\tt \dashrightarrow \frac{d}{s} = \frac{24}{18 + x}$

Our Equation become,

$\tt \dashrightarrow \frac{24}{18 - x} - \frac{24}{18 + x} = 1.$

$\tt \dashrightarrow24 [ \frac{1}{18 - x} - \frac{1}{18 + x} ]= 1.$

$\tt\dashrightarrow24 [ \frac{(18 - x) - (18 + x)}{(18 - x)(18 + x)} ]= 1.$

$\tt\dashrightarrow24 [ \frac{ \cancel{18} - x \cancel{- 18} - x}{(18 - x)(18 + x)} ]= 1.$

$\tt\dashrightarrow \frac{ - 2x}{{(18 ) }^{2} - {(x )}^{2} } = \frac{1}{24} .$

$\tt\dashrightarrow 324 - {x}^{2} = - 48x.$

$\tt\dashrightarrow {x}^{2} + 48x - 324 = 0.$

Compare with General Equation,

$\tt a{x}^{2} + bx + c = 0.$

Where as,

• a = 1.
• b = 48.
• c = -324.

Taking number, 324.

$\begin{array}{r | l} 2 & 324 \\ \cline{2-2} 2 & 162 \\ \cline{2-2} 9 & 81 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

$\tt\dashrightarrow {x}^{2} + 54x - 6x- 324 = 0.$

$\tt\dashrightarrow x(x + 54) - 6(x + 54) = 0.$

$\tt\dashrightarrow (x - 6)(x + 54) = 0.$

Either,

$\tt\dashrightarrow x + 54 = 0.$

$\tt\dashrightarrow x = - 54.$

And,

$\tt\dashrightarrow x - 6 = 0.$

$\tt\dashrightarrow x = 6.$

$\rule{200}1$

Note : Speed never be negative,

So, Ignore

$\tt\dashrightarrow \red{ x \neq - 54.}$

Therefore, the speed of stream be 6 km/h.

Answer 2

QuEsTiOn :-

A motor boat whose speed is 18km/h in still water takes 1 hour more to go 24km up stream than to return down stream to the same spot . Find the speed of the stream..

Given -

Speed of boar in still water = 10km/h

Time taken = 1 hour

Distance = 24 km

SoLuTiOn :-

Let the speed of the stream = x km/h

Speed of boat upstream = Speed of boat in still water - speed of stream = 18 - x

Speed of boat downstream = Speed of boat in still water + speed of stream = 18 + x

We know that =>

${\purple{\boxed{\large{\bold{Time = \frac{Distance}{Speed} }}}}}$

According To Question

$\implies \frac{24}{18 - x} - \frac{24}{18 + x} = 1 \\ \\ \implies \frac{24(18 + x) - 24(18 - x)}{(18 - x)(18 + x)} = 1 \\ \\ \implies432 + 24x - 432 + 24x = (18 - x)(18 + x) \\ \\ \implies48x = 18(18 +x) - x(18 + x) \\ \\ \implies48x = 324 + 18x - 18x - {x}^{2} \\ \\ \implies - {x}^{2} + 324 = 48x \\ \\ \implies - {x}^{2} + 324 - 48x = 0 \\ \\ \implies {x}^{2} + 48x - 324 = 0 \\ \\ \implies {x}^{2} + 54x - 6x - 324 = 0 \\ \\ \implies \: x(x + 54) - 6(x + 54) = 0 \\ \\ \implies(x - 6)(x + 54) = 0 \\ \\ \implies \: x - 6 = 0 \: and \: x + 54 = 0 \\ \\ \implies \: x = 6 \: and \: x = - 54 \\ \\ speed \: cannot \: be \: negative \: . \\ \\ So ,\: - 54 \: will \: be \: neglect.$

AnSwEr :-

${\red{\boxed{\large{\bold{Speed \:of \:stream\:= \: 6km/h }}}}}$