Gantt chart: critical path

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Quick Questions

Shade in the A or B circle for each question.

1. Which describes the critical path of a project?

A The chain of tasks with the shortest total time, which finishes first

B The longest chain of dependent tasks, which sets the earliest possible finish date

2. Task A (3 days) leads to Task B (4 days). Task C (2 days) runs alongside them. All three start together. Which tasks are on the critical path?

A A and B, because the chain takes 7 days and C takes only 2

B C only, because it is the shortest and finishes first

3. A task on the critical path is delayed by 2 days. What happens to the project?

A The finish date moves back by 2 days unless time is made up elsewhere

B Nothing changes because other tasks will absorb the delay automatically

4. What does it mean if a task has float (slack)?

A It can start late or run longer, within limits, without delaying the project

B It must be finished first because it is the most important task

5. Which statement about float is correct?

A Tasks on the critical path have the most float

B Tasks on the critical path have zero float

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1A(2) -> B(3) -> D(4) = 9 days		AA task with 5 days of float can slip 1 day without delaying the project, so the finish date does not change.
2Float = 3 days		BCritical task: 4 days -> 6 days, Project: 9 days -> 11 days
3The critical path decides the shortest possible project length, because it is the longest chain of dependent tasks		CPath 1: 9 days, Path 2: 6 days -> Project = 9 days
4If a critical task is delayed, the whole project finish date is delayed by the same amount		DThe critical path is the longest chain of dependent tasks, not the shortest, because the longest chain sets the minimum project time.
5Critical path = shortest chain of tasks (6 days)		EA non-critical task can be delayed by up to 3 days without delaying the project finish
6Task off the critical path delayed 1 day (float 5) -> Project finishes 1 day late		FAdding the durations along a chain of dependent tasks to find its total length; the longest chain is the critical path

Definitions

critical path

Fill in the Blanks

Complete each line of code by filling in the missing parts.

pathLength ← taskA + taskB _ taskD

pathOne ← 3 + 4 + 2 criticalPath ← ___(pathOne, pathTwo)

float ← latestStart _ earliestStart

IF float = _ THEN SET onCriticalPath ← TRUE END IF

IF taskDelay > 0 AND ______________ THEN projectEnd ← projectEnd + taskDelay END IF

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A A Plan 3d start

B B Build 4d after D

C C Docs 2d after A

D D Test 1d after B,C

E Critical path: A,B,D = 8d

Question 2

A Path 1: A-B-D = 3+4+1 = 8d

B Path 2: A-C-D = 3+2+1 = 6d

C Critical path = Path 2, 6d

Question 3

A A=3d, B=4d, C=2d, D=1d

B A-B-D = 3+4+1 = 7d

C A-C-D = 3+2+1 = 6d

D Float of C = 8 - 6 = 2d

Question 4

A Critical path = shortest path

B A-B-D = 8d, A-C-D = 6d

C Project needs at least 8d

Question 5

A C is off the critical path

B C has 2d float

C C can slip 2d safely

D C slips 3d: finish +3d

Answer Key

Gantt chart: critical path

Section A: Quick Questions

B — The longest chain of dependent tasks, which sets the earliest possible finish date

A — A and B, because the chain takes 7 days and C takes only 2

A — The finish date moves back by 2 days unless time is made up elsewhere

A — It can start late or run longer, within limits, without delaying the project

B — Tasks on the critical path have zero float

Section B: Match the Pairs

A(2) -> B(3) -> D(4) = 9 days → Adding the durations along a chain of dependent tasks to find its total length; the longest chain is the critical path

Float = 3 days → A non-critical task can be delayed by up to 3 days without delaying the project finish

The critical path decides the shortest possible project length, because it is the longest chain of dependent tasks → Path 1: 9 days, Path 2: 6 days -> Project = 9 days

If a critical task is delayed, the whole project finish date is delayed by the same amount → Critical task: 4 days -> 6 days, Project: 9 days -> 11 days

Critical path = shortest chain of tasks (6 days) → The critical path is the longest chain of dependent tasks, not the shortest, because the longest chain sets the minimum project time.

Task off the critical path delayed 1 day (float 5) -> Project finishes 1 day late → A task with 5 days of float can slip 1 day without delaying the project, so the finish date does not change.

Section C: Definitions

critical path — The longest chain of dependent tasks in a project. It sets the shortest possible finish time, and any delay to a task on it delays the whole project. Tasks off it have float.

Section D: Fill in the Blanks

pathLength ← taskA + taskB + taskD

pathOne ← 3 + 4 + 2
criticalPath ← MAX(pathOne, pathTwo)

float ← latestStart - earliestStart

IF float = 0 THEN
    SET onCriticalPath ← TRUE
END IF

IF taskDelay > 0 AND onCriticalPath THEN
    projectEnd ← projectEnd + taskDelay
END IF

Section E: Spot the Error

B — Build cannot depend on Test, because Test comes after Build and this would create a loop. Build should start after A, so the line is 'B Build 4d after A'. The critical path A,B,D is only valid with correct dependencies.

C — The critical path is the longest chain of dependent tasks, not the shortest. Path 1 takes 8 days, so it is the critical path.

B — 3 + 4 + 1 is 8, not 7. A wrong total could make you pick the wrong longest path. The line should be 'A-B-D = 3+4+1 = 8d'.

A — The critical path is the longest chain of dependent tasks. It sets the shortest possible project finish time. The line should say 'longest path'.

D — C has 2 days of float, which absorbs the first 2 days of delay. A 3 day slip only delays the project by 1 day (3 - 2). The line should be 'C slips 3d: finish +1d'.