Races and Games question bank (Quantitative Aptitude)

In a race of $300 \text{ m}$,$A$ beats $B$ by $15 \text{ m}$ or $5 \text{ s}$. $A$'s time over the course is:

$A$'s speed is $1 \frac{1}{2}$ times of $B$'s speed. In a race,$A$ gives $B$ a start of $300 \, m$. How long should the race course be so that both reach the winning post simultaneously? (in $m$)