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    Question

    Two runners A and B stand at opposite ends M and N of a

    straight track. A begins toward N at (x – 6) km/h. Four hours later, B starts toward M at (x + 6) km/h. They meet at the midpoint of MN. If MN = 576 km, determine how long A would take to cover the entire MN.
    A 18 hrs Correct Answer Incorrect Answer
    B 20 hrs Correct Answer Incorrect Answer
    C 12 hrs Correct Answer Incorrect Answer
    D 24 hrs Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Distance covered by A in 4 hours = 4(x – 6) km Remaining distance = 576 – 4(x – 6) = 576 – 4x + 24 = (600 – 4x) km Time of meet after B starts = (600 – 4x)/(2x) hours According to question, [(600 – 4x)/(2x)] × (x + 6) = 576/2 (600x + 3600 – 4x² – 24x) = 576x ⇒ –4x² + 3600 = 0 x² = 900 x = 30 Speed of A = 30 – 6 = 24 km/h Therefore, required time = 576/24 = 24 hours

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