Time and Work
What is Time and Work?
The amount of work an individual or group can complete in one unit of time.
Key formula / rule: Work Done
Key points
- Understand the relationship between work, rate, and time.
- Calculate the combined work rate of multiple individuals.
- Solve problems involving men, women, boys, and their efficiencies.
- Apply the concept to problems involving pipes and cisterns.
Common exam trap
Confusing rate of work with time taken.
Definitions
- Term
Rate of Work
- Meaning
The amount of work an individual or group can complete in one unit of time.
- Term
Efficiency
- Meaning
The relative capability of individuals to perform work; higher efficiency means a faster rate of work.
- Term
Combined Work
- Meaning
The total work done when multiple individuals or entities work together on a task.
Learning objectives
Understand the relationship between work, rate, and time.
Calculate the combined work rate of multiple individuals.
Solve problems involving men, women, boys, and their efficiencies.
Apply the concept to problems involving pipes and cisterns.
Formulae
- Name
Work Done
- Note
Rate is the amount of work done per unit time.
- Expression
Work = Rate × Time
- Name
Individual Rate
- Note
If a person completes a work in 'Time' units.
- Expression
Rate = 1 / Time
- Name
Combined Rate (Working Together)
- Note
Sum of individual rates when working in the same direction.
- Expression
Combined Rate = R1 + R2 + R3 + ...
- Name
Net Rate (Working Against)
- Note
For pipes filling and draining simultaneously.
- Expression
Net Rate = Ratein - Rateout
- Name
Total Work (using LCM)
- Note
Assigning LCM as the total units of work simplifies calculations.
- Expression
Total Work = LCM(T1, T2, ...)
Prerequisites
Basic Arithmetic (fractions, percentages)
LCM and HCF
Understanding of ratios and proportions.
Common mistakes
Confusing rate of work with time taken.
Incorrectly adding or subtracting rates when individuals work together or against each other.
Assuming constant work rate for all individuals without considering efficiency differences.
Calculation errors, especially with fractions.
Keywords
Time and Work
Rate of Work
Efficiency
Pipes and Cisterns
LCM
Combined Effort
Work Done
Practice preview
15 men can complete a work in 8 days. How many men are required to complete the same work in 6 days?…
medium
If A is twice as good a workman as B, and together they finish a piece of work in 14 days, in how many days can A alone finish the work?…
easy
A can do a piece of work in 10 days and B in 15 days. They work on alternate days, with A starting the work. In how many days will the work be completed?…
medium