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! ⏰
BETA
