Question
A race track is in the shape of a rectangle with length
of 80 metres and area of 4500 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.Solution
Area of the track = length of track x breadth of track = 80 x breadth of track = 4500 So, breadth of track = 4500 ÷ 80 = 56.25 So, perimeter of the track = (80 + 56.25) x 2 = 272.5 metres So, speed of the car = (272.5/10) = 27.25 m/s Relative speed of the car with respect to the person = 27.25 + 5 = 32.25 m/s So, distance between the car and the person, 3 seconds before they cross each other = 32.25 x 3 = 96.75 metres
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