Question

    A race track is in the shape of a rectangle with length

    of 13 metres and area of 1300 m2. A car takes 10 seconds to make one lap around the perimeter of this track. If the car and a person whose speed is 5 m/s, started moving at the same time along the perimeter of the track but in opposite directions, then find the distance between the car and the person, 3 seconds before they cross each other.
    A 82.8 metres Correct Answer Incorrect Answer
    B 72.8 metres Correct Answer Incorrect Answer
    C 62.8 metres Correct Answer Incorrect Answer
    D 55.8 metres Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Area of the track = length of track x breadth of track = 13 x breadth of track = 1300 So, breadth of track = 1300 ÷ 13 = 100 So, perimeter of the track = (13 + 100) x 2 = 226 metres So, speed of the car = (226/10) = 22.6 m/s Relative speed of the car with respect to the person = 22.6 + 5 = 27.6 m/s So, distance between the car and the person, 3 seconds before they cross each other = 27.6 x 3 = 82.8 metres

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