>>114714091): 5 cents.
3): 47 days. The question can be interpreted as a continuous process, or as a discrete process. Either way, the patch has covered at least fully half, or (what is the same) more than half, but not all of the lake, on day/iteration 47.
2): It isn't specified:
- a) whether the machines are all identical (or: fungible), each producing a complete widget by itself,
- b) whether the machines are all different (an assembly line), with no two performing the same operation, or
- c) whether the machines are mixed, with some being identical, and others being distinct from one another.
Consider a). If 5 identical machines (separately) produce 5 widgets in 5 minutes, then each machine produces one widget per every 5 minutes, and the machines collectively produce 5 widgets every 5 minutes. Scaling this, 100 of the same machines would produce 100 widgets in 5 minutes.
Consider b). If 5 distinct machines collectively produce 5 widgets in 5 minutes, then scaling this to 100 machines would entail 20 identical 5-machine assembly lines, each line producing 5 widgets in 5 minutes, or again, 100 machines would collectively produce 100 widgets in 5 minutes. Note that this says nothing about the TAC time for a given machine's step.
Consider c). This would again be some mixed arrangement, but the details are immaterial. A group of 5 machines produces 5 widgets in 5 minutes. Scaling the same arrangement to 100 machines would entail 20 5-machine lines of the same type, with 100 machines again producing 100 widgets in 5 minutes.
So, the cases all resolve to 100 machines producing 100 widgets in 5 minutes at all events. Tacit in this is the mere scaling of whatever 5-machine arrangement exists, by 20.
