In a race of $200\text{m}$, $A$ beats $B$ by $45\text{m}$ or $9$ seconds. Find the time taken by $A$ to complete the race.

"$A$ beats $B$ by $45\text{m}$ or $9$ seconds" means that $B$ takes $9$ seconds to cover the remaining $45\text{m}$.Speed of $B=\frac{\text{Distance}}{\text{Time}}=\frac{45}{9}=5\text{m/s}$.Total time taken by $B$ to finish the $200\text{m}$ race:
$${\text{Time}}_B=\frac{200}{5}=40\text{sec}$$
Since $A$ beats $B$ by $9$ seconds:
$${\text{Time}}_A={\text{Time}}_B-9=40-9=31\text{sec}$$