I might not understand the problem correctly, but it sounds like "exponential" is unnecessary information. We only need to know the average time between jobs is 3 months, so she is working 11 months and not working 3 months.
Monica works on a temporary basis. The mean length of each job she gets is 11 months. If the amount of time she spends between jobs is exponential with mean 3 months, then in the long run what fraction of time does she spend working?