Question

Two cars start together in the same direction from the same place. The first goes with uniform speed of $10$ km/h. The second goes at a speed of $8$ km/h in the first hour and increase the speed by $\frac{1}{2}$ km each succeeding car overtake the first car if both cars go non-stop?

• A. $4$ hours
• B. $9$ hours
• C. $15$ hours
• D. $18$ hours

Answer 1

Answer: (B)

$9$ hours

Let the second car over takes the first car after $n$ hours
$\therefore$ Distance covered by first car $=$ Distance covered by second car.
$\Rightarrow {10}_n=8+[8+\frac{1}{2}]+[8+\frac{2}{2}]...+[8+\frac{n-1}{2}]$
$\Rightarrow {10}_n=8n+\frac{1}{2}[1+2+...+(n-1)]$
$\Rightarrow {10}_n=8n+\frac{1}{2}\left(\frac{n(n-1)}{2}\right)$
$\Rightarrow 2n=\frac{1}{4}(n^2-n)$

$\Rightarrow 8n=n^2-n$

$\Rightarrow n^2=9n$
$\Rightarrow n=9$ hours