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Hours to finish a job when two work together
A batch of parts takes a master 12 hours to make alone, or an apprentice 18 hours alone. If the master works 3 hours first and then the two work together, how many more hours are needed to finish?
Answer
27/5 hours (5.4 hours)
Step-by-step
- 1/12 × 3 = 1/4Find the part of the job the master finishes first
- 1 - 1/4 = 3/4Find the part of the job still left to do
- 1/12 + 1/18 = 5/36Find how much the two finish together in one hour
- (3/4) ÷ (5/36) = 27/5Divide the work left by the combined hourly rate to get the time
Why it works
The master's 3 hours finish 1/4 of the job, the remaining 3/4 is done at a combined rate of 5/36 per hour, and 3/4 ÷ 5/36 = 27/5 hours.
Common mistakes
- Adding 12 and 18 hours and then subtracting 3.
- Using 1/12 + 1/18 = 1/30 for the combined rate (the denominators must be added as reciprocals).
- Forgetting that the master's first 3 hours already reduced the work left.