New 55% Off on All Courses - Enroll Now! Click Here

    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.
    A 18 km/h Correct Answer Incorrect Answer
    B 22 km/h Correct Answer Incorrect Answer
    C 25 km/h Correct Answer Incorrect Answer
    D 30 km/h Correct Answer Incorrect Answer

    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.

    Practice Next