Interesting task on Poisson process

Question

Child is playing computer game. The moments of appearance of enemies forms poisson point process with $\lambda =400 $ enemies per hour. Child kills an enemy with probability $\frac{1}{4}$ (he do it instantly). In order to pass the level he needs kill $100$ enemies . I need to find the distribution of time of passing level. So actually I don’t know how attempt this problem.