Third worker joining a pipe build

Working alone, Alice needs $120$ minutes to build a pipe and Bob needs $100$ minutes. They start one pipe together; after $40$ minutes Charlie joins them, and the three finish $10$ minutes later. How many minutes would Charlie need on his own?

120. Measure the job as $600$ units, so Alice does $5$ and Bob $6$ per minute. In $40$ minutes they make $440$ units; the last $160$ units take $10$ minutes at $16$ per minute, so Charlie adds $5$ per minute and alone needs $600/5=120$ minutes.