Question

A motorboat whose speed is 18 km/h in still water takes 1 hour more to
go
24 km upstream than to return downstream to the same spot. Find the
speed of the stream.
ए मोटरबोट व्होस स्पीड इज 8 किलोमीटर इन स्टिल वॉटर टैक्स ​

Answer 1

AnswEr :

Speed of stream is 6 km/hr.[We can't take speed as negative]

Step-by-step explanation :

We're given that the speed of boat in still water is 18km/hr. The same boat takes more 1 hour to go 24 km upstream than to return downstream to the same spot.

So, here we've to find out the speed of stream.

Let us assume that the speed of stream is 'x'.

In order to calculate the speed of stream we need to know the following things :

• Speed of boat upstream.

• Speed of boat down stream.

• Total time taken for upstream.

Accordingly, we know that,

• Speed of the boat Upstream = Speed of boat in still water - speed of stream = 18 - x

• Speed of the boat Downstream = Given speed of boat in still water + speed of stream = 18 + x

• Total time taken for Upstream = Time taken for downstream + 1

Now, let's form the linear equation to know the actual speed of boat.

$: \implies\sf \: \: \dfrac{Distance_{upstream}}{Speed_{Downstream}} = \dfrac{Distance_{upstream}}{Speed_{Downstream}} + 1$

$: \implies\sf \: \: \dfrac{24}{18 - x} = \dfrac{24}{18 + x} + 1$

$: \implies\sf \: \: \dfrac{24}{18 - x} = \dfrac{24}{18 + x} + \dfrac{1(18 + x)}{18 + x}$

$: \implies\sf \: \:24(18+x)=24(18 - x)+(18 - x)(18+x)$

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

$: \implies\sf \: \: {x}^{2} + 54x - 6x - 324 = 0$

$: \implies\sf \: \: (x + 54)(x - 6) = 0$

$: \implies\sf \: \: { \boxed{ \sf{ \purple{x = - 54}}}} \: \: or \: \: { \boxed{ \sf{ \pink{x = 6}}}}$

As speed of the stream cannot be negative the correct answer is x = 6 km/hr.

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

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

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream is 6 km /hr.

Please make my answer brainliest.