Question

A motorboat goes downstream in a river and covers the distance between two coastal towns in five hours.
covers this distance upstream in six hours. If the speed of the stream is 2 km/h, find the speed of the boat
still water?
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Answer 1

SOLUTION :-

Given that,

Speed of the stream = 2 km/h

Let the speed of the boat in still water be x km/h .

Speed of the boat in downstream = ( x + 2 ) km/h

Speed of the boat in upstream = ( x - 2 ) km/h

Distance covered by the motor boat in downstream = 5 ( x + 2 ) km

Distance covered by the motor boat in upstream = 6 ( x - 2 ) km

According to the question,

Distance travelled by the motor boat in downstream and upstream are equal.

$\longrightarrow\sf 5(x+2)=6(x-2) \\\\\longrightarrow 5x+10=6x-12 \\\\\longrightarrow 5x-6x = -12-10 \\\\\longrightarrow -x = -22 \\\\\longrightarrow \bf x = 22$

Speed of the boat in still water = 22 km/h

Answer 2

Given :

Distance covered by motorboat downstream in 5 hours.

And it covers same distance upstream in 6 hours.

The speed of water is 2km/hr.

To find :

The speed of the boat in still water.

Solution :

Let's assume the speed of the boat in still water as x km/h.

Speed of water(given) = 2km/h

Speed of boat in downstream = (x+2) km/h

So, Distance covered in 5 hrs :

D= Speed x Time

=5 x (x + 2) km

= 5x + 10 km

•Speed of boat in upstream = (x - 2) km/h

So, Distance covered in 6 hrs : Speed x Time

= 6 x (x - 2) km

= 6x 12 km

Now, As is given that the boot covers the same distance upstream and downstream also.

Thus,

6x - 12 = 5x + 10

6x - 5x = 10 + 12

x = 22

Therefore x = 22 km/h that is the speed of water in still water.

Checking the answer :

•Distance covered in 5 hours in downstream = Speed x Time

D = 5(x + 2)

= 5(22 + 2)

= 110 + 10

= 120 km

•Distance covered in 6 hours in upstream = D=Speed x Time

= 6(x - 2)

= 6(22 - 2)

= 132 - 12

= 120 km.

Thus, in both the cases ,the distance is equal .Hence the Solution is correct.

hope it's help u.....