Question

The speed of a river current is 3 km/h . A boat takes the same time to travel 15km upstream as it does to travel 18 km downstream. Find the speed of the boat in still water .​

Answer 1

In the above Question , the following information is given - .

The speed of a river current is 3 km/h .

A boat takes the same time to travel 15km upstream as it does to travel 18 km downstream.

To find -

Find the speed of the boat in still water .

Solution -

Let us assume that the required speed of the boat in still water is x kmph .

Now ,

The speed of a river current is 3 km/h .

So ,

When this boat travels downstream -

Net Speed Downstream -

=> ( x + 3 ) kmph

So ,

When this boat travels upstream -

Net Speed upstream -

=> ( x - 3 ) kmph

Now ,

Speed = [ Distance / Time ]

The boat takes the same time to travel 15km upstream.

Let the time taken to cover this distance be t hours .

( x - 3 ) = 15 / t ........ { 1 }

The boat takes the same time to travel 18km downstream.

( x + 3 ) = 18 / t .......... { 2 }

Now ,

Divide equation 1 by equation 2

=> [ x - 3 ][ x + 3 ] = [ 5 / 6 ]

=> 5 ( x + 3 ) = 6 ( x - 3 )

=> 5x + 15 = 6x - 18

=> x = 15 + 18

=> x = 33 kmph .

Hence , the required speed of the boat in still water is 33 kmph .

_________

Answer 2

$\huge\sf\pink{Answer}$

☞ Speed of boat in still water is 33 km/h

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Speed of a river current is 3 km/h

✭ A goat takes the same time to travel 15 km upstream as it does to travel 18 km downstream

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

➠ Speed of boat in still water?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Let us assume the speed of boat in still water as x km/h

Now,

In Upstream the speed of the boat is given by,

$\small\textsf{Speed of Boat = Speed of boat in still water - speed of river current}$

➢ Speed of boat in upstream = x - 3

In Downstream the speed of the boat is given by,

$\small\textsf{Speed of boat = Speed of boat in still water + speed of river current}$

➳ Speed of boat in downstream = x + 3

We know that,

$\sf Speed = \dfrac{Distance}{Time}$

❍ Now to travel upstream,

➠ $\sf (x-3) = \dfrac{15}{t} \qquad -eq(1)$

Now travelled downstream,

➠ $\sf (x+3) = \dfrac{18}{3}\qquad -eq(2)$

$\bullet\underline{\textsf{According to question}}$

Div EQ(1) by EQ(2)

➝ $\sf \dfrac{(x+3)}{(x-3)} = \dfrac{5}{6}$

➝ $\sf 5(x+3) = 6(x-3)$

➝ $\sf 5x+15 = 6x-18$

➝ $\sf 15+18 = 6x-5x$

➝ $\sf \orange{x = 33 \ km/h}$

$\rule{170}3$