Question
A boat travels in a river where
the current flows at a speed of 5 km/h. The total time taken by the boat to go from point 'P' to point 'Q' and return to point 'P' is 24 hours. The distance between points 'P' and 'Q' is 350 km. Determine the speed of the boat in still water.Solution
ATQ, {350/(x + 5)} + {350/(x - 5)} = 24 Or, 350 X (x - 5) + 350 X (x + 5) = 24 X (x + 5) X (x - 5) Or, 350(x - 5 + x + 5) = 24(x²- 25) Or, 700x = 24x²- 600 So, 24x²- 700x - 600 = 0 Or, 12x²- 350x - 300 = 0 Or, 12x²- 360x + 10x - 300 = 0 Or, 12x(x - 30) + 10(x - 30) = 0 Or, (x - 30)(12x + 10) = 0 So, x = 30 or x = -(5/6) Since, speed cannot be negative. So, x = 30.
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