A new feature was added during the Wild West update. Certain jobs could be rushed after most of the job is complete. Continue on to find out the details.
Updated: job manager info
The basics are that most tasks (jobs assigned from the task list) can be rushed once 90% of the time has transpired. For example, when there’s only 6 minutes left on a 60 minute job, the donut rushing icon will change to the word “FREE”. Tap this to rush (complete) the task for free instead of spending 2 Donuts.
Free rushing does not apply beyond a task remaining time that is over 2 hours and 0 seconds. Tasks as long as 24 hours (or longer) will not be rushing the last 10% but a much smaller percentage.
Free rushing only applies to tasks that are listed in a character’s task list, and only those that reward Money. Any jobs started from elsewhere, such as Springfield Heights buildings, the recycle buildings, the moonbounce, and event specific buildings, are not available for rushing.
Free rushing does not affect Krustyland. Non-character tasks, like crops on Cletus’ Farm, Channel 6 broadcasts, et al. are also not affected.
Lastly, free rushing can be performed using the job manager, but is shown as zero donuts.
TSTO, Stat! 
When you free a character that in on the book task (required on the left hand panel), will it’s consider complete or it won’t be counted at all?
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As far as I can understand your question, the answer is that “required tasks” (those assignable from the left hand panel) can be rushed, as long as the reward is Money. If they’re event-specific tasks that reward event currency, then no.
I hope that helps, or ask again.
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