Mathematics · Discrete Mathematics

Critical-Path Activity Free Float activity early finish time Solver

Rearrange the critical-path activity free float relationship and solve for activity early finish time.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
activity early finish time18
Reconstructed activity free float2

Calculation steps

  1. Use b=a−c with activity free float=2 and earliest successor start time=20.
  2. activity early finish time=18.
  3. Substitution into c=a−b reconstructs 2.

Understand Critical-Path Activity Free Float: solve activity early finish time

One idea, three depths

Choose how deeply to explain Critical-Path Activity Free Float: solve activity early finish time

Critical-Path Activity Free Float: solve activity early finish time: Rearrange the critical-path activity free float relationship and solve for activity early finish time.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Critical-Path Activity Free Float: solve activity early finish time to answer this question: rearrange the critical-path activity free float relationship and solve for activity early finish time? Enter activity free float and earliest successor start time; the calculator shows activity early finish time. For example: earliest successor start time=20 and activity early finish time=18 produce activity free float=2. The answer tells you activity early finish time.

Age 15Explain it to a 15-year-oldConnect it to the formula

Free float is the delay available before affecting the earliest start of a successor. This page isolates activity early finish time and verifies it in the original relationship. The rule is b=a−c. Its input values are activity free float, earliest successor start time, and the main result is activity early finish time. For example: earliest successor start time=20 and activity early finish time=18 produce activity free float=2.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated critical-path activity free float: solve activity early finish time relation over the valid real-number domain stated below. The implemented relation is b=a−c, evaluated from activity free float, earliest successor start time to produce activity early finish time. Free float is the delay available before affecting the earliest start of a successor. This page isolates activity early finish time and verifies it in the original relationship. For multiple successors use the minimum eligible successor early start.

Inputs and valid domain

  • activity free float must be a finite real number.
  • earliest successor start time must be a finite real number.

Important boundary: For multiple successors use the minimum eligible successor early start.

The formula

b=a−c

How the calculator works through it

It substitutes activity free float, earliest successor start time into the formula and exposes every numerical step above. The main output is activity early finish time, accompanied by Reconstructed activity free float.

Read the result correctly

The activity early finish time is the direct answer to “rearrange the critical-path activity free float relationship and solve for activity early finish time.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

earliest successor start time=20 and activity early finish time=18 produce activity free float=2.

Where this model stops being reliable

For multiple successors use the minimum eligible successor early start.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Critical-Path Activity Free Float: solve activity early finish time works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Critical-Path Activity Free Float: solve activity early finish time uses b=a−c. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Sets, membership and finite collections

    Sets provide the objects and membership rules that give Critical-Path Activity Free Float: solve activity early finish time its discrete meaning.

    Review this foundation about 6 min

Optional enrichment

  • Ordered arrangements

    Permutations connect Critical-Path Activity Free Float: solve activity early finish time to systematic counting and arrangement problems.

    Review this foundation about 5 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read activity free float, earliest successor start time.
  2. Evaluate the principal relationship: b=a−c.
  3. Return activity early finish time and check the domain conditions described above.
Python
            from math import *

def critical_path_free_float_solve_b(c, a) -> float:
    return (a - c)

assert abs(critical_path_free_float_solve_b(2, 20) - 18) < 1e-6 * max(1.0, abs(18))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double critical_path_free_float_solve_b(double c, double a) {
    return (a - c);
}

int main(void) {
    const double expected = 18;
    const double actual = critical_path_free_float_solve_b(2, 20);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double critical_path_free_float_solve_b(double c, double a) {
    return (a - c);
}

int main() {
    constexpr double expected = 18;
    const double actual = critical_path_free_float_solve_b(2, 20);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double critical_path_free_float_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global critical_path_free_float_solve_b
section .text

critical_path_free_float_solve_b:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-16]
    subsd xmm0, [rbp-8]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = critical_path_free_float_solve_b(c, a)
    result = (a - c);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, a_] := (a - c);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Critical-Path Activity Free Float activity early finish time Solver. MW SysArc Tools. https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-activity-early-finish-time-solver

MLA 9

MW SysArc. “Critical-Path Activity Free Float activity early finish time Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-activity-early-finish-time-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Critical-Path Activity Free Float activity early finish time Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-activity-early-finish-time-solver.

Harvard

MW SysArc (2026) ‘Critical-Path Activity Free Float activity early finish time Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-activity-early-finish-time-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_critical_path_free_float_solve_b_2026,
  author = {{MW SysArc}},
  title = {Critical-Path Activity Free Float activity early finish time Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-activity-early-finish-time-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Critical-Path Activity Free Float activity early finish time Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-activity-early-finish-time-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Critical-Path Activity Free Float: solve activity early finish time do?

Rearrange the critical-path activity free float relationship and solve for activity early finish time.

How does the Critical-Path Activity Free Float: solve activity early finish time work?

The calculator applies b=a−c. Free float is the delay available before affecting the earliest start of a successor. This page isolates activity early finish time and verifies it in the original relationship.

What can I learn from the Critical-Path Activity Free Float: solve activity early finish time?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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