Time and Work
About 6 min · Elementary Mathematics · English
Time worked out from the lesson's 404 words at 150 words a minute, plus a minute for each question.
The core principle is simple: if you know how long someone takes to complete a job, you can calculate their work rate per unit time. Problems may test your ability to combine work rates when multiple people or machines work together, or when they work in alternating patterns.
Key ideas
- Work as Unity: The total work is always assumed to be 1 unit (or 100%) unless stated otherwise. This standardization makes calculations uniform across all problems.
- Work Rate (Efficiency): If a person completes work in n days, their one-day work (rate) is 1/n. If A does a job in 10 days, A's rate = 1/10 per day.
- Combined Work Rate: When multiple people work together, their rates add. If A works at 1/10 per day and B at 1/15 per day, together they work at (1/10 + 1/15) per day.
- Man-Days Concept: Total work can be expressed as (number of people) × (number of days). If 5 men complete work in 12 days, the work = 60 man-days. This same work can be done by 10 men in 6 days.
- Negative Work (Pipes): In pipe problems, filling pipes contribute positive work while emptying/leak pipes contribute negative work. Net rate = (sum of filling rates) – (sum of emptying rates).
Quick reference
- If A takes a days alone, A's daily rate = 1/a; combined rates always add.
- Joint time for two workers = (product of individual times)/(sum of individual times).
- Total work = (number of workers) × (number of days) when efficiency is constant.
- In pipe problems: net rate = filling rate – emptying rate; watch for positive/negative.
- Alternating work: calculate full-cycle work first, then handle the remainder separately.
Check yourself: 3 questions
1. A can complete a work in 12 days and B can complete the same work in 18 days. If both A and B work together, in how many days will they complete the work?
2. 15 men can complete a piece of work in 20 days. After 5 days, 5 more men join them. In how many more days will the work be completed?
3. Two pipes A and B can fill a tank in 30 minutes and 40 minutes respectively. A pipe C can empty the full tank in 60 minutes. If all three pipes are opened together, in how many minutes will the tank be filled?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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