TL;DR: The critical path is the longest sequence of dependent activities — it sets the project's minimum duration. Activities on it have zero float. Any delay on the critical path delays the project end date by the same amount.
The critical path is the longest path through the project network from start to finish, measured in time. It determines the earliest possible project completion date. Every activity on the critical path has zero total float — delay any one of them and the project end date slips by exactly that many days.
Common trap: "The critical path has the most activities." Wrong. It has the most time. A single 90-day activity beats a chain of twenty 4-day activities on any parallel path. The bank's wrong answers regularly offer "the path with the most tasks" as a distractor.
Total Float: how much an activity can slip without delaying the project end date. Formula: LS − ES (Late Start minus Early Start) or LF − EF (Late Finish minus Early Finish). Activities on the critical path have TF = 0.
Free Float: how much an activity can slip without delaying its immediate successor. Formula: ES(successor) − EF(activity). Free float is always ≤ total float.
| Type | Formula | Delays what? |
|---|---|---|
| Total Float | LS − ES (or LF − EF) | Project completion |
| Free Float | ES(next) − EF(this) | Immediate successor only |
| Project Float | Deadline − Critical Path Duration | Contract/imposed deadline |
Yes — and this is a high-frequency exam scenario. If a non-critical activity slips long enough to consume all its float, it becomes critical and a new critical path emerges. The project now has two (or more) critical paths, which increases schedule risk because there are more sequences that can delay the end date.
The bank's trap: the wrong answer says "the schedule baseline must be updated immediately." Wrong first move — first assess the impact and communicate it; a change request comes after analysis, not before.
When the critical path needs to shorten:
| Technique | How it works | Trade-off |
|---|---|---|
| Crashing | Add resources (people, money, overtime) to critical path activities | Increases cost; quality risk if rushed |
| Fast Tracking | Overlap activities that were planned sequentially | Increases risk; rework likely if dependencies were sequential for a reason |
Exam cue: if the scenario says "budget is fixed," crashing is usually off the table. If it says "the dependency is only preferential, not mandatory," fast tracking is the answer.