Two concepts are needed to solve this algebraically
- 1) Rate is always the inverse of the time it takes to do 1 job. For instance if I take 5 days to do a job, then my rate is 1/5 of the job per day.
- 2) When machines work together simultaneously, their combined rate is the sum of their individual rates.
when the machines work simultaneously, according to concept #2, their combined rate will be the sum of their individual rate. Thus their combined rate is 1/k + 1/m + 1/p. We know that their combined time is 24 minutes, so according to concept #1, their combined rate can also be expressed as the inverse, or 1/24 jobs per minute. This is how the book derives the equation
- 1/k + 1/m + 1/p = 1/24
- 1/k + 1/36 = 1/24
-Patrick
