The current is a stream moves at a speed of 2 km/hr. A boat travels 12 km upstream and 12 km downstream in a total of 8 hours. What is the speed of the boat in still water?

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llltkl | College Teacher | (Level 3) Valedictorian

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Let the speed of the boat in still water be b km/hr.

Speed of the current in the stream is 2 km/hr.

Therefore, speed of the boat in the upstream journey=(b-2)km/hr and downstream journey is (b+2)km/hr.

Time required in the upstream journey=12/(b-2) hrs

and time required in the downstream journey=12/(b+2) hrs

By the condition of the problem,

`12/(b-2)+12/(b+2)=8`

`rArr (3(b+2+b-2))/((b+2)(b-2))=2`

`rArr 6b=2b^2-8`

`rArr b^2-3b-4=0`

`rArr b^2-4b+b-4=0`

`rArr (b-4)(b+1)=0`

`rArr b=4, -1`

Since b is speed of the boat, it has to be non-negative.

So, b=4 km/hr.

Speed of the boat in still waters is 4 km/hr.

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