Question

Two cars start together in the same direction and the same place .The first goes with a speed of 10kmph and the second goes with the speed of 8kmph in the first hour and increases the speed by 0.5 kmph in every succeeding hour after how many hours will the second car overtake the first car if both go non stop.

Answer 1

Speed of the first car = 10 km/h
Speed of the second car:
In the first hour = 8 km/h
In the second hour $=(8+\frac{1}{2})=\frac{17}{12}km/h$
In the third hour $=(\frac{17}{2}+\frac{1}{2})=9km/h$
$\therefore$ The numbers $8,\frac{17}{2},9\dots \dots$ are in AP
In which $a=8,d=\frac{1}{2}$ and $n=x$
Let the second car overtake the first car in x hours.
$\therefore$ Distance covered by the second car in x hours
$\Rightarrow 10x=$Sum of x numbers in above AP $=S_x$
$\therefore 10x=\frac{x}{2}[2a+(x-1\left)d\right]\therefore 10x=\frac{x}{2}[2\times 8+(x-1\left)\frac{1}{2}\right]\therefore 10x=\frac{x}{2}[2\times 8+(x-1\left)\frac{1}{2}\right]\therefore \frac{10\text{/}x\times 2}{\text{/}x}=16+\frac{x}{2}-\frac{1}{2}\therefore 2\times 20=32+x-1\therefore 40-31=x\Rightarrow x=9$
$\therefore$ The second car overtakes the first car in 9 hours.