Two cars starf simultaneously from the same place and in same direction . The first car moves with a uniform speed of 10 km/h . The second car moves at a speed of 8km/hr in the first hour and then increases its speed by 0.5 km/hr in each succeeding hour . If both the cars move non stop , then how long will it take for the second car to overtake?

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Solution

Member since Apr 11 2014

Consider the second car overtake the first car by t hours.

∴ Distance covered by first car = distance covered by second car.

10t = 8 + ( 8 + 1/2 ) + ( 8 + 2/2) + ( 8 + 3/ 2) + --------------------+ ( 8 + (t - 1) / 2)

10t = 8t + (1/2) [ 1 + 2 + 3 + ................+ ( t - 1)]

2t = (1/2)[ t (t -1) / 2]

8t = [ t² - t ]

t² = 9t

∴ t = 9 as t ≠ 0

∴ the second car overtake the first car by 9 hours.

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