Time and Work Calculator
Solve for
Enter how long each worker takes to complete the job alone. Find total time working together.
How Time & Work Calculations Work
Every time and work problem is based on one principle: Work = Rate × Time. Here's the logic step by step.
01
Work Rate
If a worker finishes a job in N days, their rate is 1/N per day. This is the fraction of the total job they complete each day.
Rate = 1 ÷ Time
02
Combined Rate
When multiple workers collaborate, their rates simply add up. The total time is the reciprocal of the combined rate.
T = 1 ÷ (R₁ + R₂ + …)
03
Workers Needed
To finish by a deadline T, divide each worker's solo time D by T. Round up to the nearest whole number.
Workers = D ÷ T
04
Pipes & Cisterns
Filling pipes add to the net rate; emptying pipes subtract. The cistern fills when net rate is positive.
T = 1 ÷ (Σfill − Σempty)
Solved Examples
Click any row to load it into the calculator above.
| Type | Problem | Answer | Try |
|---|---|---|---|
| Find Time | A takes 10 days, B takes 15 days. Together? | 6 days | |
| Find Workers | Each worker takes 12 days. Finish in 3 days? | 4 workers | |
| Work Done | A=10d, B=20d working together for 4 days? | 60% | |
| Pipes | Pipe A fills in 6h, Pipe B empties in 12h? | 12 hours | |
| Find Time | A=6d, B=8d, C=12d. Together? | ≈ 2.67 days |
Time & Work Formula Reference
| What to Find | Formula | Notes |
|---|---|---|
| Combined time (2 workers) | T = (A × B) ÷ (A + B) | A, B = individual times |
| Combined time (n workers) | T = 1 ÷ (1/T₁ + 1/T₂ + …) | Add all rates, take reciprocal |
| Workers needed | W = D ÷ T_target | D = days each alone; round up |
| Work done in time t | W = t × (1/T₁ + 1/T₂ + …) | Fraction of total job |
| Remaining work | Rem = 1 − W | 1 = full job = 100% |
| Pipe fill time | T = 1 ÷ (Σfill − Σempty) | Emptying rates subtracted |
Frequently Asked Questions
What is a time and work problem?
A time and work problem asks how long one or more workers (or pipes) take to finish a task. Each worker's rate = 1 ÷ (individual time). Combined rates add together.
How is combined work rate calculated?
If A takes a days and B takes b days, combined rate = 1/a + 1/b per day. Time together = 1 ÷ (1/a + 1/b), which simplifies to (a × b) ÷ (a + b).
What is the formula for time and work?
Work = Rate × Time. A worker completing a job in N days has rate 1/N per day. Rates of multiple workers simply add together.
Can I solve pipe and cistern problems?
Yes. Use the Pipes & Cisterns tab. Filling pipes add to the net rate; emptying (outlet) pipes subtract. Net rate determines fill time.
What units are supported?
Each input lets you choose days, hours, or minutes independently. All values are normalized before computing, so you can freely mix units.
Is this calculator free?
Yes — completely free, no account, no limits.