Joel lives in Berkeley. He mainly commutes by public transport, i. e., bus and BART. He hates waiting while transferring, and he usually plans his trip so that he can get on his next vehicle immediately after he gets off the previous one (zero transfer time, i. e. if he gets off his previous vehicle at 7:00am he gets on his next vehicle at 7:00am). Tomorrow, Joel needs to take an AC Transit bus from his home stop to the Downtown Berkeley BART station, then take BART intoSan Francisco. Required:
a. The bus arrives at Joel’s home stop every 22 minutes from 6:05am onwards, and it takes 10minutes to get to the Downtown Berkeley BART station. The train arrives at the station every 8 minutes from 4:25am onwards. What time is the earliest bus he can take to be able to transferto the train immediately?

b. Joel has to take a Muni bus after he gets off the train in San Francisco. The commute time on BART is 33 minutes, and the Muni bus arrives at the San Francisco BART station every 17minutes from 7:12am onwards. What time is the earliest bus he could take from Berkeley to ensure zero transfer time for both transfers? If all bus/BART services stop just before midnight, is it the only bus he can take that day?