$A$'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 $m$)

In a $500\, m$ race,the ratio of speeds of two contestants $A$ and $B$ is $3: 4$. $A$ has a start of $140\, m$. Then,$A$ wins by (in $m$)

In a race of $600\, m$,$A$ can beat $B$ by $60\, m$ and in a race of $500\, m$,$B$ can beat $C$ by $50\, m$. By how many $m$ will $A$ beat $C$ in a race of $400\, m$?

In a game,$A$ can give $B$ $25$ points in $75$ and $C$ $18$ points in $90$. How many points can $C$ give $B$ in a game of $120$?

In a $1000 \, m$ race,$A$ can beat $B$ by $80 \, m$ and $B$ can beat $C$ by $60 \, m$. In the same race,$A$ can beat $C$ by (in $m$):

Four runners started running simultaneously from a point on a circular track. They took $200$ seconds,$300$ seconds,$360$ seconds,and $450$ seconds to complete one round. After how much time do they meet at the starting point for the first time? (in seconds)