HI and thanks for asking your question here at the forum!

The posts so far have provided correct math, so:

1. Your process (cycle time = 5 min.) can not only keep up with current customer demand (takt = 6 min.), but will begin to build up inventory - either somewhere mid-process as WIP (work in proces) or at the end as finished goods. Either way, in lean terms, that's waste, as you will be making more than demand called for. From an accounting perspective, it's costing you more to sit there too!

There are follow on exercises and tools which would allow you to arrive at a more optimal match between cycle and takt. This involves load balancing and perhaps reconfiguring your staffing, but those would be "other" questions for the classes you're taking.

2. In this case the math works nicely (that means is easy for me!) For your overall process, the total cycle time, or completion time, is determined by the slowest step. So in this case, it's 18 minutes. Take that against a takt time of 15 minutes, and you find you cannot keep up with demand. At this point, you would need to conduct a value add/non-vlaue add analysis and then probably a line (load) balancing exercise to improve your cycle times so you can meet takt. Given that none of the 4 operators has a cycle time less than takt, probably not an easy puzzle.

Hope this helps.

Cheers!