Time and Work - Formula Sheet
⏰ Time and Work - Formula Sheet
🎯 Basic Formulas
Work Rate
Work = Rate × Time
Rate = Work / Time
Time = Work / Rate
Individual Work
If A can do work in x days:
A's rate = 1/x work per day
Combined Work
If A and B work together:
Combined rate = 1/x + 1/y
Time = 1 / (1/x + 1/y) = (x × y) / (x + y)
📊 Multiple Workers
Three Workers
A + B + C together: 1/x + 1/y + 1/z
Time = 1 / (1/x + 1/y + 1/z)
LCM Method
Total work = LCM of individual times
Individual work = Total work / Individual time
🔢 Special Cases
Work and Leave
A works for x days, then B joins
Work done by A alone = x/a
Remaining work = 1 - x/a
Efficiency Change
New rate = Original rate × Efficiency factor
New time = Original time / Efficiency factor
Fractional Work
If A does 1/3 work, B does 2/3 work:
A's time = Total time / 3
B's time = Total time / (3/2) = 2 × Total time / 3
⚡ Quick Calculations
Common Combinations
1/a + 1/b = (a + b) / (a × b)
1/2 + 1/3 = 5/6
1/3 + 1/6 = 1/2
Work Distribution
If A : B = m : n efficiency
Then work ratio = m : n
Time ratio = 1/m : 1/n
📝 Problem Types
Together and Apart
- Find combined time: Use combined rate formula
- Find individual time: Use work distribution
- Work and leave: Calculate partial work first
Pipes and Cisterns
Inlet pipes: Add rates (fill)
Outlet pipes: Subtract rates (empty)
Net rate = Fill rate - Empty rate
Efficiency Problems
More workers → Less time (inverse proportion)
Efficiency ↑ → Time ↓ (inverse proportion)
🔍 Important Notes
- Work rate = Work/Time
- Combined rate = Sum of individual rates
- Total work can be any convenient number
- LCM method avoids fractions
- Efficiency and time are inversely proportional
Master Time & Work - Rate is the key concept! ⏰
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