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Work Together Calculator

Math Calculators

Combined work time · head start · fill & drain pipes · back-solve

Quick Answer

Work Together Calculator: Combined work time · head start · fill & drain pipes · back-solve. Work Together Calculator uses standard math formulas to compute accurate results instantly.

Time working together
2 d
33.33% less time than the quickest person alone
Combined rate50%
Quickest alone3 d
Time saved33.33%
In minutes2,880 min

Share of work done by each

Work share

A 66.67%67 (66.7%)B 33.33%33 (33.3%)

Common work-problem models

ModelFormulaExample
Two workerst = a·b ÷ (a+b)3 天 + 6 天 → 2 天
Three workerst = 1 ÷ (1/a+1/b+1/c)2h + 3h + 6h → 1 h
Head startT = m + (1−m/a) ÷ (1/a+1/b)甲 4 天先做 1 天，乙 6 天 → 共 2.8 天
Fill & draint = a·b ÷ (b−a)（需 b>a）进 4h 出 6h → 12 h
Back-solveb = a·t ÷ (a−t)（需 a>t）合作 2 天 + 甲 3 天 → 乙 6 天
Alternating days每个周期完成 1/a+1/b，逐周期累加甲 2 天乙 4 天轮流 → 2.5 天
Work problems treat the whole job as 1: rate = 1 ÷ solo time, and together time = 1 ÷ sum of rates. Exam trick: set the job to the LCM of the times (3 d and 6 d → 6 units; A does 2 units/day, B does 1, so together = 2 d by mental math). Pipes are "negative rate" cooperation — if the drain is not slower than the fill pipe, the tank never fills. Together time is always shorter than the quickest solo time; if your result breaks this rule, the inputs are wrong.

Calculation steps

  1. 1Rate = 1 / solo time: A 33.33%, B 16.67% (per input unit)
  2. 2Combined rate = 50% per unit
  3. 3Together time = 1 ÷ combined rate = 2 d

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How to Use

  1. Enter values or expressions: type directly into the Work Together Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Work Together Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Combined work time · head start · fill & drain pipes · back-solve.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Work Together Calculator formula

Work Together Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Work Together Calculator?
Open the page and fill in the input fields — results update automatically. Combined work time · head start · fill & drain pipes · back-solve.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

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Results provided by this tool are for reference only and do not constitute professional advice.