Build the network from the predecessor table, compute earliest times by a forward pass and latest times by a backward pass, then find the path with zero float throughout.

Step 1 — Set up the network's events. Event 1 (start) → A and B both begin here (no predecessors). A (4 days) finishes at event 2; C (predecessor A) runs from event 2 to event 3 (2 days). B (3 days) finishes at event 2 as well only if it shares a tail with A — but since A and B have no shared predecessor relationship stated, and D depends on B while C depends on A, event 1 is the common start for both A and B, with A leading to the event where C starts, and B leading to the event where D starts; C and D both feed into event 4, from which E (3 days) runs to the final event 5.

Step 2 — Forward pass (earliest event times, $E$). $E_1=0$ (start). $E_2 = E_1+4=4$ (after A). Also treat B's completion event similarly: $E$ at B's finish $=E_1+3=3$. $C$ runs from A's finish, duration 2: reaches $E=4+2=6$. $D$ runs from B's finish, duration 5: reaches $E=3+5=8$. Both C and D feed into the event before E, so that event's earliest time is the larger of the two incoming paths: $E_4 = \max(6,8)=8$. Finally $E_5 = E_4+3 = 8+3=11$ (project's earliest finish).

Step 3 — Identify the two paths from start to finish explicitly. Path A→C→E: duration $4+2+3=9$ days. Path B→D→E: duration $3+5+3=11$ days.

Step 4 — Backward pass (latest event times, $L$), starting from $L_5=E_5=11$. Working back through E (duration 3): the event before E must have $L=11-3=8$. Working back along D (duration 5) from that event: B's finish event needs $L=8-5=3$. Working back along C (duration 2) from the same shared event: A's finish event needs $L=8-2=6$. …

Comparing every start-to-finish path's total duration directly, as in the Independent check, is a fast way to identify the critical path in a small network with only a couple of paths, a …

Assuming the path with the most activities (or the first-listed path) is automatically the critical one is a common misconception — the critical path is defined purely by having the longest total duration, regardless of how many individual activities make it up; here, both p …