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Grade: 10
        
Two cars start together 'm' the same direction from the same place. The first goes with uniform speed 10km/h. The second goes at a speed of 8km/h m the first hour and increases the speed by 1/2km m each succeeding hour .After how many hours will the second car overtake the first car if both cars goes non stop.
8 months ago

Answers : (1)

Arun
13856 Points
							Dear Kushal
Let the second car overtakes the first car after n hours.
Hence
Distance covered by first car = distance covered by second car
10n = 8 + (8 +1/2) + (8 + 2/2) + (8+3/2) + .......+(8 + n-1/2)
10 n = 8n + 1/2 [1 +2 +3 + 4+.......(n-1)]
2n = (1/2)[n(n-1)/2]
4n = n(n-1)/2
8 n = n² - n
n² - 9n = 0
n = 9
Hence answer is 9 hours
Regards
Arun (askIITians forum expert)
8 months ago
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