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GMAT Quant
Work and Machine Rates
Convert completion times into work rates and combine changing workers correctly.
Core model
Treat one complete job as work = 1.
If a worker finishes the job in t hours, the rate is 1/t job per hour.
A 5-hour worker
- Total work
- 1 job
- Time
- 5 hours
- Rate
- 1/5 job per hour
- Work in 2 hours
- 2/5 job
Combined work
Workers combine by adding rates, not completion times.
If A works at 1/a job per hour and B at 1/b, together they work at 1/a + 1/b.
Example: A needs 6 hours; B needs 4 hours.
- A rate
- 1/6
- B rate
- 1/4
- Together
- 5/12 job/hour
- Together time
- 12/5 = 2.4 hours
Changing workers
When the team changes, split the timeline into phases.
Compute work completed during the first phase, subtract from 1, then use the new rate on the remaining work.
Common traps
- 01Adding 6 hours + 4 hours instead of adding rates.
- 02Forgetting that the job total can be defined as 1.
- 03Using the old combined rate after one worker leaves.
- 04Mixing minutes and hours.
Mini application
Try this: A can finish a job in 8 hours and B in 8 hours. They work together for 2 hours.
What fraction of the job remains?
Solution
One-half of the job remains.
Together they work at 1/8 + 1/8 = 1/4 job per hour. In 2 hours they finish 1/2.
Remember this
Convert time into rate first.
Once every worker is expressed as work per unit of time, the rest is ordinary rate x time.