Project Duration from an Activity Network

Mediumproject controlscritical pathscheduling
An activity-on-node schedule has activity A (6 days) followed by both B (4 days) and C (3 days). B is followed by D (5 days) and C is followed by E (2 days). Both D and E precede F (4 days), which is followed by G (2 days). The critical path duration is most nearly:
  1. A15 days
  2. B17 days
  3. C21 days
  4. D26 days
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Answer: C. 21 days

Enumerate the paths through the network. A-B-D-F-G = 6 + 4 + 5 + 4 + 2 = 21 days. A-C-E-F-G = 6 + 3 + 2 + 4 + 2 = 17 days. The critical path is the longest, so the project duration is 21 days and the second path carries 4 days of float. Adding every activity duration gives 26 days, which would only apply if no work ran in parallel.
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