Multiple choice

A train 300 metres in length passes a signal post in y seconds, and crosses a 480-metre-long bridge in (y + 8) seconds. Determine the time the train will take to overtake a cyclist moving in the same direction at 36 km/hr.

  1. y seconds

  2. 2y seconds

  3. y + 1 seconds

  4. y – 2 seconds

  5. y + 4 seconds
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C Correct answer
AI explanation

Using the formula speed = distance / time, the speed of the train is 300 / y meters per second. When crossing the bridge, the total distance is the train length plus the bridge length, so 300 / y equals (300 + 480) / (y + 8). Solving 300(y + 8) = 780y gives 2400 = 480y, so y = 5 seconds. The cyclist's speed of 36 kilometers per hour equals 10 meters per second. The relative speed for overtaking is (300 / 5) - 10 = 50 meters per second. The time to overtake the cyclist is the train's length divided by this relative speed, which is 300 / 50 = 6 seconds. Since y = 5, this result equals y + 1 seconds.

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