Question

Question:-
☆A motor boat whose speed is 24 km/hr in still water takes 1 hr more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.

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Answer 1

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☆A motor boat whose speed is 24 km/hr in still water takes 1 hr more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.

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Let speed of the stream be x km / hr

Speed of the boat in still water = 24 km / hr

Speed of the boat in upstream = ( 24 - x ) km / hr

Speed of the boat in downstream = ( 24 + x ) km / hr

Distance between the places is 32km

$time \: to \: travel \: in \: upsteam \: = \frac{d}{24 - x} hr$

$time \: to \: travel \: in \: downsteam \: = \frac{d}{24 + x} hr$

Difference between timings = 1 hr

time of upstream journey = time of downstream journey + 1hr

$therefore \: \frac{32}{24 - x} = \frac{32}{24 + x} + 1$

$\frac{32}{24 - x} - \frac{32}{24 + x} = 1$

$\frac{768 + 32x - 768 + 32x}{(24 - x)(24 + x)} = 1$

$64x = 576 - {x}^{2}$

${x}^{2} + 64x - 576 = 0$

On factoring , we get

( x + 72 ) ( x - 8 ) = 0

So X = -72 or 8 ( speed of the stream cannot be negative )

Therefore , speed of stream is 8 km / hr .

Answer 2

$\large\underline{\sf{Given- }}$

• Speed of boat in still water is 24 km/hr.

• Distance covered is 32 km in upstream as well as in downstream.

• Time taken in upstream is 1 hour more than downstream.

$\large\underline{\sf{To\:Find - }}$

• Speed of the stream.

$\large\underline{\sf{Solution-}}$

• Let speed of the stream be 'x' km per hour.

According to statement,

Given that,

• Speed of motor boat in still water = 24 km/hr.

So,

• Speed of boat in downstream = (x + 24) km/hr

and

• Speed of boat in upstream = (24 - x) km/hr

• Distance to be covered is 32 km.

Now,

$\sf \: Time \: taken \: to \: cover \: 32 km \: in \: downstream \: ( t_1) = \dfrac{32}{24 + x}$

and

$\sf \: Time \: taken \: to \: cover \: 32 km \: in \: upstream \: ( t_2) = \dfrac{32}{24 - x}$

According to statement,

$\dashrightarrow \: \dfrac{32}{24 - x} - \dfrac{32}{24 + x} = 1$

$\rm :\longmapsto\:\dfrac{32(24 + x) - 32(24 - x)}{(24 + x)(24 - x)} = 1$

$\rm :\longmapsto\:\dfrac{32 \times 24 + 32x - 32 \times 24 + 32x}{ {24}^{2} - {x}^{2} } = 1$

$\rm :\longmapsto\:64x = 576 - {x}^{2}$

$\rm :\longmapsto\: {x}^{2} + 64x - 576 = 0$

$\rm :\longmapsto\: {x}^{2} + 72x - 8x - 576 = 0$

$\rm :\longmapsto\:x(x + 72) - 8(x + 72) = 0$

$\rm :\longmapsto\:(x - 8)(x + 72) = 0$

$\bf\implies \:x = 8 \: \: \: or \: \: \: x = - 72 \: \: (rejected)$

$\bf \: Hence, \: speed \: of \: stream \: is \: 8 \: km \: per \: hour$

Basic Concepts :-

Stream – The moving water in a river is called a stream.

Upstream – If the boat is flowing in the opposite direction to the stream, it is called upstream. In this case, the net speed of the boat is called the upstream speed.

Downstream – If the boat is flowing along the direction of the stream, it is called downstream.