Physics, asked by ayazkhan1746, 1 year ago

The rate of stream is 4 kmph. A boat goes 6 kms and returns back to the starting point in 2 hrs. Then the speed of the boat in still water?

Answers

Answered by santy2
2

Let the speed of the boat is still water be x.

The boat goes upstream and downstream.

In both upstream and downstream it covers a distance of 6 km each.

The total time taken is 2hrs.

Speed upstream = (x - 4) km/h

Speed downstream = (x + 4) km/h

Time = Distance/speed

Total time = 6/(x + 4) + 6/(x - 4)

We equate this to 2 as follows:

2 = 6/(x + 4) + 6/(x - 4)

(x - 4)(x + 4)2 = 6(x - 4) + 6(x + 4)

(x^2 - 16)2 = 6x - 24 + 6x + 24

2x^2 - 32 = 6x + 6x

2x^2 - 12x - 32 = 0

Divide through by 2 we have :

x^2 - 6x - 16 = 0

The roots are - 8 and +2

Expanding the equation we have :

x^2 - 8x + 2x - 16 = 0

x(x - 8) + 2(x - 8) = 0

(x + 2)(x - 8) = 0

x = - 2 or 8

Since speed cannot be negative we take the positive value of x which is 8.

The speed of the boat in still water is thus :

8 km/h

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