Question

Two cars start together in same direction from same place.The first goes with uniform speed of 10 km per hour.The second goes at a speed of 8 km per hourin first hour and increases the speed by by 1/2 km in each succeeding hour.After how many hours will the second car overtake the first if both cars go non stop.

Answer 1

Speed of second car is in the form of an A.P, with speed increasing as 1/2 km/hr.
8 , 8.5 , 9 , 9.5, 10 , 10.5 , 11, 11.5, 12
The first car moves at a constant rate of 10 km/hr
1st hour: 2nd car covers 2 kms less than 1st
2nd hour: covers 1.5 kms less
3rd hour: covers 1 km less
4th hour: covers 0.5 km less
5th hour: speed of both car same
Hence till 5 hours, second car is behind 1st car by: 2+1.5+1+0.5 = 5 km
6th hour: second car covers 0.5 km more than 1st
7th hour: 1 km more than 1st
8th hour: 1.5 km more than 1st
9th hour: 2 km more than 1st
Thus now the distance covered by both cars become equal.
Hence second car will overtake 1st car after 9 hours
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Answer 2

Step-by-step explanation:

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