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Q.

On a city road, the last traffic light glows green for 60 s and red for 120 s. The range of speeds of vehicles is from 503ms−1 to 2009ms−1 in a group. The speed of each  vehicle is constant. It is found that at a distance x from traffic light, then the successive groups pushing through traffic light place will become indistinguishable. The value of x (in km) is _______________.

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answer is 8.

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Detailed Solution

x=2009t=503(t+120) or 200t9=50t3+503×120 or 200t−150t9=2000 or 50t=2000×9∴ t=2000×950=360s∴ x=2009×360=200×40=8000m=8km
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On a city road, the last traffic light glows green for 60 s and red for 120 s. The range of speeds of vehicles is from 503ms−1 to 2009ms−1 in a group. The speed of each  vehicle is constant. It is found that at a distance x from traffic light, then the successive groups pushing through traffic light place will become indistinguishable. The value of x (in km) is _______________.