Question

    A man rows 45 km downstream and 27 km upstream in a

    total of 6 hours. If the speed of the stream is 3 km/h, find the speed of the boat in still water.
    A 28 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 27 Correct Answer Incorrect Answer
    D 18 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let boat speed in still water = b km/h Downstream speed = b + 3, upstream speed = b − 3 Equation: [45/(b+3)] + [27/(b−3)] = 6 45(b−3) + 27(b+3) = 6(b²− 9) 45b − 135 + 27b + 81 = 6b²− 54 72b − 54 = 6b²− 54 6b²− 72b = 0  ⇒ 6b(b−12) = 0  ⇒ b = 12.

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