finish date or the early start date from the late start date. The numbers will be the same. If not, you made a math error. Total Float = Late Start – Early Start (or Late Finish - Early Finish) FREE FLOAT Free float is the number of days an activity can be delayed without taking float away from the next activity. Another way of saying the same thing is that free  float  is  the  number  of  days  an  activity  can be delayed without delaying the early start date of the  next  activity.  To  calculate  the  free  float  for  an activity, you subtract any lag and the early finish for the activity from the early start for the next activity. To calculate the free float for activity 1020 in figure 2-13 you would take the early start for activity 1050, subtract any lag between 1020 and 1050 (zero in this case), and subtract the early finish for activity 1020 (11 - 0 - 10= 1). Free float for activity 1020 is 1 day. You can see that delaying activity 1020 by 1 day will not  delay  activity  1050  from  its  early  start  date. Delaying activity 1020 by 2 days will delay the start of activity 1050 until day 12 and will reduce the float for  activity  1050  by  1  day  (to  zero,  in  this  case). Delaying activity 1020 by more than 2 days will delay the project completion date because 1020 has only 2 days  of  total  float. Free Float = Early Start (next activity) – Lag (if any) –  Early  Finish* CRITICAL PATH Looking  at  activity  1020  in  figure  2-13  you  see you could start that activity as early as day 3 or as late as day 5. Now subtract 3 from 5 and enter 2 days as the total float. Where the early start and late start are the same there is no float. No float means you have to start that activity on its early start date. It cannot be delayed  without  delaying  the  project  completion. Activities  with  no  float  are  said  to  be  critical.  The first and last activities will always be  critical and there will be a critical path of activities between them. The critical path in figure 2-13 is 1010-1040-1060-1070. The   critical   path   allows   management   to   focus attention on those activities that cannot slip. DIFFERENT  LOGIC  TYPES All examples shown so far have used finish-to- start  logic.  This  logic  type  requires  an  activity  to finish before the next one can start. There are two other types of logic relationships that are frequently encountered.  They  are  the  start-to-start  (S/S)  and finish-to-finish  (F/F).  S/S  is  where  the  start  of  the second activity is dependent on the start of the first activity.  F/F  is  where  the  finish  of  the  second  activity is   dependent   on   the   finish   of   the   first   activity. Finish-to-start logic will give you the longest total project duration and is the most common logic type used in the NCF. The S/S and F/F logic can be used   to   compress   (shorten)   the   schedule.   This compression is often used in the execution phase of the  project  to  catch  up.  These  logic  relationships  also can  be  used  to  plan  repetitive  work  such  as  roadways or sewer lines. For a sewer line you wouldn’t want to excavate the entire ditch before starting to lay pipe. NOTE: Equations marked with an (*) are changed with different types of logic (S/S or F/F). Start-to-Start Forward Pass: Early start + Lag = Early start (next activity) Backward  Pass:  Late  start  –  Lag  = Late start (preceding  activity) Free Float: Early start (next activity) – Lag – Early start Finish-to-Finish Forward Pass: Early finish + Lag = Early finish (next activity) Backwwd Pass: Late finish –  Lag  = Late finish (preceding  activity) Free Float: Early finish (next activity) – Lag – Early finish The general rule to follow with different types of logic is to always  follow  your  logic  connectors. Figure 2-14 is an example of a network with lag times (between activities B and F, C and D, C and E). Figure 2-15 is an example of logic relationships. Using the  formulas,  work  through  the  calculations. LEVEL III BARCHARTS Having determined the construction schedule on the precedence network, you must now transfer that 2-17