A factory has two machines. Each machine independently works for an exponentially dis- tributed time with a mean of 20 days before breaking down. Only one machine can be serviced at a time, and when both machines are broken, Machine 1 is serviced rather than Machine 2. When a machine is being serviced at timet, the probability that it is repaired before timet+his 2h+o(h). Once a machine is repaired, it is as good as new, and works for another exponentially distributed time with a mean of 20 days before breaking again.

(a) In the long-run, what fraction of the time is Machine 1 broken?

(b) In the long-run, what fraction of the time is Machine 2 broken?