For a 10-day project, activity B ' s duration is three days, and activity C’s duration is two days What is the duration of activity A if activities B and C are performed in parallel?

The total duration of a project is determined by the longest path of sequential activities, known as the critical path. When activities are performed in parallel, the time required to complete that segment of the project is equal to the duration of the longest activity in the parallel set. In this scenario, Activity B (3 days) and Activity C (2 days) are in parallel, so this segment takes 3 days to complete. To find the duration of Activity A, subtract the duration of the parallel segment from the total project duration: 10 days (total) - 3 days (parallel segment) = 7 days.

A. 3 days: This is the duration of the parallel block of activities (B and C), determined by the longer of the two, not the duration of activity A.
B. 5 days: This is the incorrect sum of the durations of the parallel activities B and C. Durations of parallel activities are not added together.
D. 10 days: This is the total duration for the entire project, not the duration for the individual activity A. ---

1. Project Management Institute. (2021). A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Seventh Edition. Project Management Institute, Inc. In the Planning Performance Domain, section 2.5.3, "Estimating," the guide discusses the aggregation of estimates. The underlying logic for schedule aggregation requires that parallel workstreams are accounted for by their longest duration, not their sum, which is a foundational concept of the Critical Path Method.

2. Project Management Institute. (2017). A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Sixth Edition. Project Management Institute, Inc. Section 6.5.2.1, "Schedule Network Analysis," describes the Critical Path Method. This method calculates the longest path of activities, where the duration of parallel paths is determined by the activity with the longest duration within that path. The total project duration is the sum of durations on this critical path.

3. Kerzner, H. (2017). Project Management: A Systems Approach to Planning, Scheduling, and Controlling (12th ed.). Wiley. Chapter 12, "Scheduling," details the Precedence Diagramming Method (PDM), explaining that when multiple activities precede a single activity (a path convergence), the start of the next activity is dependent on the completion of the longest preceding parallel activity. This principle is directly applied in the question's calculation.