Question:
Two cars start together in the same direction from the same place. The first goes with uniform speed of 10km/hr. The second goes at a speed of 8km/hr in the first hour and increases its speed by 1/2 km/hr each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop
Answer:
Let the second car overtakes the first car after t hours.
Now, distance covered by the first car = distance covered by the second car
=> 10t = 8 + (8 + 1/2) + (8 + 2/2) + ............{8 + (t - 1)/2}
=> 10t = {8 + 8 + 8+...........t times} + (1/2)*{1 + 2 + 3 + ..........(t - 1)}
=> 10t = 8t + (1/2)*{t(t - 1)/2}
=> 10t - 8t = (t2 - t)/4
=> 2t = (t2 - t)/8
=> 8t = t2 - t
=> t2 - 8t - t = 0
=> t2 - 9t = 0
=> t(t - 9) = 0
=> t = 0, 9
Since t can not be equal to 0,
So t = 9
Hence, after 9 hours, the second car will overtake the first car.
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