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      Question

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

      of 30 metres and area of 900 m2. A car takes 15 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 39 metres Correct Answer Incorrect Answer
      B 29 metres Correct Answer Incorrect Answer
      C 19 metres Correct Answer Incorrect Answer
      D 44 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 = 30 x breadth of track = 900 So, breadth of track = 900 ÷ 30 = 30 So, perimeter of the track = (30 + 30) x 2 = 120 metres So, speed of the car = (120/15) = 8 m/s Relative speed of the car with respect to the person = 8 + 5 = 13 m/s So, distance between the car and the person, 3 seconds before they cross each other = 13 x 3 = 39 metres

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