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jatin vora

· started a discussion

· 1 Months ago

why common difference 1/2 (Question: 184411.0 )

as the questions says speed of second car increases by 1 km/hr...
so the A.P should be 8+9+10.......+n
so common difference in this case should be =9-8 = 1

Question:
Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 km/hr. The second goes at a speed of 8 km/hr in the first hour and increases the speed by  1/2 km/hr in each succeeding hour. After how many hours will the second overtake the first car if both cars go non - stop ? 
Options:
A) 16 hours 
B) 9 hours 
C) 18 hours 
D) 24 hours 
Solution:

Ans: (b)

Suppose the second car overtakes the first car after x hours. Then the two cars travel the same distance in x hours. 

Distance travelled by first car in x hours 

= 10x kms 

Distance travelled by second car in x hours 

= Sum of x terms of A.P with first term 8 and common difference 1/2.

i.e. x/2 [2.8+(x-1) 1/2]

=   \(\cfrac{x(x+31)}{4}\)

ATQ 10x =  \(\cfrac{x(x+31)}{4}\)

x = 9 hours

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