In short: In work problems, the total work is workers × time, and it stays the same for the same job. So more workers finish faster: if 4 people take 6 hours, 8 people take 3 hours.
Before you start
- Multiplying and dividing, including fractions like .
- Adding and subtracting fractions with different denominators (see the Fractions unit).
- Minutes and hours: h min.
Person-hours
When the job changes size
If the job is bigger or smaller, scale the work too.
Rates: filling and emptying
When things work at the same time, think about how much of the job is done in 1 hour (or 1 minute).
- Workers x time
- Stays the same for the same job
- More workers, less time
- Scale the work
- Fraction of the job per hour
- Working together: add
- Draining: subtract
- Together is faster than alone
Quick summary
- Total work workers time. It stays the same for the same job.
- More workers means less time (inverse proportion).
- If the job size changes, scale the total work.
- A rate is the fraction of the job done per hour or minute. Add rates for things working together, subtract for things working against.
- When you need a whole number of people, round up.
Quiz
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Try 3 questions now
3 people take 4 hours to build a shed. How long do 2 people take?
- A hours
- B 3 hours
- C 6 hours
- D 8 hours
Show answer
C: 6 hours
Work person-hours. .
2 people paint a fence in 6 hours. How long would 4 people take?
- A 3 hours
- B 12 hours
- C 6 hours
- D 1.5 hours
Show answer
A: 3 hours
Work person-hours. .
3 girls take hours to paint an attic. How long would 1 girl take?
- A hours
- B 7 hours
- C hours
- D hours
Show answer
C: hours
hours.