Question

A motorboat whose speed is 18 kilometre per hour in still water takes 1 hour more to go 24 kilometre upstream then to return down stream to the same spot find the speed of the stream.
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Answer 1

$\large \ { \fcolorbox{purple}{WHITE}{ \: \textsf{\ \ \ \ \ \ \ \ \ \pink{answer}\ \ \ \ \ \ \ \ \ }}}$

Given parameters:

The speed of the motorboat in still water =18 kmph

Let us consider

The speed of the stream = s

Speed of boat upstream = Speed of a boat in still water – the speed of a stream

Speed of boat upstream = 18 – s

Speed of boat downstream = Speed of a boat in still water + speed of a stream

Speed of boat downstream = 18 + s

Time is taken for upstream = Time taken to cover downstream + 1

time =distance/speed

DistanceupstreamSpeedupstream=DistancedownstreamSpeeddownstream+1

24/ (18 – s) = [24/(18 + s)] + 1

24(18+s) = 24(18−s) + (18−s)(18+s)

s2 + 48s − 324 = 0

s2 + 54s − 6s − 324 = 0

(s+54)(s−6) = 0

s = 6,−54 but s ≠−54

Since the speed of steam cannot be negative.

∴ s = 6km/hr

Answer 2

Answer:

$\huge\texttt\red{Question}$

A motorboat whose speed is 18 kilometre per hour in still water takes 1 hour more to go 24 kilometre upstream then to return down stream to the same spot find the speed of the stream.

$\huge\textbf\blue{Answer}$

• Let speed of stream be x km/h

Speed of motor boat in still water = km/

• $\texttt{upstream speed =(18-x ) }$
• $\texttt{dowmstream speed =(18+x ) }$
• $\textbf{Distance = 24 km}$

$\textbf{Time Taken for upstream}$$= \frac{24}{18 - x} hours$

$\textbf{Time Taken for downstream}$

$= \frac{24}{18 + x} hours$

$\texttt{ATQ,}$

$= > \frac{24}{18 - x} - \frac{24}{18 + x} = 1$

$= > \frac{24(18 + x - 18 +x )}{(18 - x)(18 + x)} = 1$

$= > \frac{24 \times \times x}{ {18}^{2 } - {x}^{2} } = 1$

$= > 324 - {x}^{2} = 48x$

$= > {x}^{2} + 48x \: - 324 = 0$

$= > {x}^{2} + 54x - 6x - 324 = 0$

$= > x(x + 54) - 6(x + 54) = 0$

$= > (x - 6)(x + 54) = 0$

$so$

$x + 54 = 0 \: and \: x - 6 = 0$

$\textbf{x = -54 (rejected)}$

$\texttt{hence, x = 6}$

• $\texttt{speed of streak = 6 km/h}$