Some more Probability.

$A$ is an archer whose probability of killing a target he aims at is $\frac{1}{3}$ . He wants to kill his enemy $B$ who arrives at a park everyday between $5$ pmto $6$ pm and waits there for $30$ mins from his time of arrival. Archer $A$ stays at the park for $10$ mins from his time of arrival (also between $5$ pm and $6$ pm). The probability that $B$ is killed between $5$ pm to $6$ pm is given by $\frac{a}{b}$ where $a$ and $b$ are co-prime. What is the value of $a+b$ if $A$ has only one shot?

Details: For $B$ to get killed, both $A$ and $B$ must be present at the park at the same time and the $A$ 's arrow must hit $B$ .