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
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