# The critical path and float > A forward pass and a backward pass by hand on eight tasks of the physics launch: the earliest finish, the chain with no room, and how much the other tasks can slip. - Course: [Project Management Without the Bureaucracy: Run One Project from Brief to Closure](https://productovi.com/courses/project-management-without-bureaucracy.md) - Module: Time: dependencies and the critical path - Lesson 10/32, ~26 min - Source: https://productovi.com/courses/project-management-without-bureaucracy/critical-path-and-float ## Which chain decides the date? **Alex Tutor:** Last time we found what waits for what. Today we take eight tasks of the launch, the curriculum, tutors, landing page and launch email, and find which chain decides when they can all be done. > **Eight tasks of the launch** > > Durations in working days; day 1 is Monday 2 November 2026. Times are counted in finished working days: a start at 0 means work begins on day 1, a finish at 51 means the end of day 51. > > | Task | Duration | Needs first | > |---|---|---| > | A Curriculum units drafted | 22 | none | > | B Vira's curriculum review | 10 | A | > | C Tutor sourcing and screening | 18 | none | > | D Demo lessons | 8 | B, C | > | E Tutor onboarding | 6 | D | > | F Landing page | 8 | none | > | G Booking by subject | 5 | F | > | H Launch email and ads | 5 | E, G | **Danylo:** Just add up all the durations? **Alex Tutor:** That gives 82 days, as if everything ran one after another. But A, C and F can start on the same day. You need the longest chain of tasks that wait for each other. **Alex Tutor:** That chain is the **critical path**: its length is the shortest time the work can take, and any delay on it moves the end. Two passes find it. **Alex Tutor:** Before the passes: why isn't the answer 82? > **Exercise:** The eight tasks add up to 82 working days. Why can they finish much sooner than day 82? ## The forward pass **Alex Tutor:** Forward pass: earliest start is the latest earliest finish among a task's predecessors; earliest finish is start plus duration. A runs 0 to 22, C 0 to 18, F 0 to 8. **Sofia:** B needs A, so 22 to 32. G needs F, so 8 to 13. D needs both B and C. **Alex Tutor:** Then D waits for the later of the two. Work it out. > **Exercise:** Forward pass: what is the **earliest finish** of D, the demo lessons? In working days from the start. **Sofia:** D runs 32 to 40, E 40 to 46. H needs E and G: E finishes at 46, G at 13, so H runs 46 to 51. **Alex Tutor:** So these eight tasks can finish at the earliest on day 51, Monday 11 January. Not 82. **Vira:** And which of them can't move a day without moving the 51? **Alex Tutor:** That's the backward pass. But first, the end date itself. > **Exercise:** What is the earliest finish of the whole eight-task network? ## The backward pass and float **Alex Tutor:** Backward pass: start from the end. Latest finish of the last task is 51; latest start is finish minus duration. Each task's latest finish is the earliest latest start of the tasks that wait for it. **Sofia:** H: 46 to 51. E: 40 to 46. D: 32 to 40. So B must finish by 32, and A by 22. **Alex Tutor:** And C? It only feeds D, which must start by 32. So C may finish as late as 32, start as late as 14. **Alex Tutor:** **Float** is latest start minus earliest start: how long a task can slip without moving the end. Tasks with zero float form the critical path. > **Exercise:** Which tasks have **zero float**, so they form the critical path? Select all that apply. **Sofia:** So A, B, D, E and H have zero float: 22 + 10 + 8 + 6 + 5 is 51. **Vira:** My review is on it. I knew it. **Alex Tutor:** Now C, Roman's screening: earliest start 0, latest start 14. **Danylo:** And my landing page and booking? > **Exercise:** What is the **float** of C, Roman's sourcing and screening? In working days. **Alex Tutor:** Danylo's turn: how much room does the landing page have? > **Exercise:** Now Danylo's landing page (F, 8 days, no predecessors), followed by booking by subject (G, 5 days), which H needs by day 46. What is the **float** of F? In working days. ## Float is shared **Alex Tutor:** F and G both show 33 days of float. Careful: that's one float shared along the chain, not 33 each. **Danylo:** So if the landing page takes 20 days longer, booking has only 13 left. **Alex Tutor:** Exactly. And float isn't a gift to spend: it's room for surprises. Starting late "because there's float" uses it up before anything goes wrong. **Alex Tutor:** Test the shared-float point with numbers. > **Exercise:** F (landing page) and G (booking) both show 33 days of float. The landing page runs 20 days late. How many days of float are left for booking? **Alex Tutor:** One warning. These are only eight tasks. Add the diagnostic test chain and the critical path may run somewhere else entirely. **Vira:** So my review might not even be the problem? **Alex Tutor:** It might feed a longer chain. You'll see in the case, with all seventeen tasks. **Danylo:** And when one critical task finishes early, does everything speed up? > **Exercise:** **True or false:** if a task on the critical path finishes 3 days early, the whole project always finishes 3 days early. **Sofia:** So the critical tasks get my attention every week, and the others get a check on their float. **Alex Tutor:** Now put float and the critical path to work on two delays. > **Exercise:** In the eight-task network, Roman's screening (C) runs 10 days late. A week later Vira's review (B) also runs 3 days late. What happens to the end date (day 51) in each case, and why? > **Key ideas** > > - The **critical path** is the longest chain of dependent tasks; its length is the shortest possible time (51 days here, not the 82 of all durations added). > - Forward pass: earliest start = latest earliest finish of the predecessors; earliest finish = start + duration. > - Backward pass: latest finish = earliest latest start of the successors; latest start = finish − duration. > - **Float** = latest start − earliest start. Zero float means critical: A, B, D, E, H. Roman's screening has 14 days; the landing page and booking share 33. > - Float is shared along a chain and is room for surprises, not permission to start late. - Previous lesson: [Dependencies and milestones as decision points](https://productovi.com/courses/project-management-without-bureaucracy/dependencies-and-milestones.md) - Next lesson: [Effort is not duration: when adding people helps](https://productovi.com/courses/project-management-without-bureaucracy/effort-is-not-duration.md) --- Productovi Learning. Free, no sign-up needed to read.