Time and Work

Rumman Ansari Software Engineer 2024-07-28 09:08:31 148 Share
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Table of Content:

Time and Work Formulas
Basic Concepts
Basic Formulas
Work
Rate
Time
Work Done by Multiple Entities
Combined Work Rate
Total Time
Work Efficiency
Efficiency
Work Sharing
Share of Work
Work Involving Multiple Workers
Work Done in Given Days
Example Problems
Example 1: Finding Time
Example 2: Finding Efficiency
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Time and Work Formulas

Basic Concepts

The basic concept of Time and Work problems is that work is generally considered to be 1 unit and the efficiency of a person is the amount of work done in a unit of time.

Basic Formulas

Work

Work = Rate \times Time

Rate

Rate = \frac{Work}{Time}

Time

Time = \frac{Work}{Rate}

Work Done by Multiple Entities

Combined Work Rate

Combined Work Rate = {Rate}_{1} + {Rate}_{2} + \dots + {Rate}_{n}

Total Time

If A can complete a work in $T_{A}$ days and B can complete the same work in $T_{B}$ days, then:

Total Time = \frac{T_{A} \times T_{B}}{T_{A} + T_{B}}

Work Efficiency

Efficiency

Efficiency = \frac{1}{Time Taken to Complete Work}

Work Sharing

Share of Work

If A and B together can complete a work in $T$ days and A alone can complete the work in $T_{A}$ days, then B alone can complete the work in $T_{B}$ days, where:

\frac{1}{T} = \frac{1}{T_{A}} + \frac{1}{T_{B}}

Work Involving Multiple Workers

Work Done in Given Days

If A, B, and C together can complete a work in $T$ days, then the work done by A, B, and C together in $D$ days is:

Work Done = \frac{D}{T}

Example Problems

Example 1: Finding Time

If A can complete a work in 10 days and B can complete the same work in 15 days, how long will it take for both to complete the work together?

Total Time = \frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6 days

Example 2: Finding Efficiency

If A can complete a work in 8 days, what is A's efficiency?

Efficiency = \frac{1}{8} = 0.125 units/day

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