Two cars start together in the same direction from the same place. The first goes with uniform speed of `10 k m//hdot` The second goes at a speed of `8k m//h` in the first hour and increases the speed by `1//2k m` each succeeding hour. After how many hours will the second car overtake the first car if both cars to non-stop?

Explanation

Let the number of ms be n hrs

Distance covered by `1^(st)`car=10n

Distance covered by `2^(nd)`car`=8+(8+1/2)+(8+2/2)+(8+3/2)+...+(8+(n-1)/2)`

`=8+8+8+...+ntimes+1/2(1+2+3...(n-1))`

`=8n+1/2(((n-1)*n)/2)`

`=8n+1/4(n^2-n)`

`10n=8n+1/4(n^2-n)`

`2n=1/4(n^2-n)`

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