Question

Raj and Vinay move together by their cars in the same direction from the same
place. Raj goes with a uniform speed of 10 km/h. Vinay goes with a uniform speed of
8 km/h in the first hour and increases the speed by 1/2 km in each succeeding
hour. After how many hours Vinay's car will overtake Raj's car, if both the cars

run non-stop​

Answer 1

Answer = 9 hours

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Answer 2

Answer:

9 hours

Step-by-step explanation:

It is given that,

Both Raj and Vinay move together in their respective cars in the same place

The uniform speed of Raj’s car = 10 km/hr

Vinay’s car goes with a speed of 8 km/hr for the first hr then increases by 1/2 km every hr.  

Let the Vinay’s car overtakes the Raj’s car after “n” hours.

Therefore,

[Distance covered by Raj’s car] = [Distance covered by Vinay’s car]

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

⇒ 10n = 8n + [1/2*{1 +2 +3 + 4+.......+(n-1)}]

⇒ 2n = 1/2*[n(n-1)/2]

⇒ 4n = n(n-1)/2

⇒ 8 = n - 1  

⇒ n = 8 + 1

⇒ n = 9