Time and Work
The LCM (total-units) method for time-and-work problems, combining and subtracting work rates, the man-days idea, and the standard patterns: one person leaving partway, and alternating days.
What you will be able to do
- Model a job as a fixed number of work units and each worker as a rate.
- Combine rates for people working together and subtract rates to isolate one.
- Use the man-days relationship for scaling workers, days and work.
- Solve problems where a worker joins or leaves partway through.
What is inside this lesson
- 1Work as units, workers as rates
- 2The LCM (total-units) method
- 3The man-days relationship
- 4Worked example: two people together
- 5Worked example: isolating one worker
- 6Worked example: a worker leaves partway
- 7Common mistakes
- 8Quick revision
Get Pro for full access. This is section 1 of 8; the rest of the lesson opens with Pro at onelystop.in/upgrade.
Work as units, workers as rates
A time-and-work problem is a rate problem. Treat the whole job as a fixed amount of work. If a person finishes it in d days, that person does one d-th of the job per day; that fraction is their rate.
The fraction method works, but the arithmetic is cleaner if you scale the job up to a whole number of units. Take the total work to be the lowest common multiple of the times given; each person's daily output is then a whole number.
Reading the 8 sections above is free. A free account opens the first 2 topics of every subject in full, along with flashcards and private notes.