P6 Math: Supervisor and Worker

If 1 supervisor and 3 workers are working together they will complete a task in 4 days.

If 2 supervisors and 1 worker are working together they will take 3 days to complete the task. How long will it take to complete the task if 1 worker is to work alone on the task ?

Solution

Let s = amount of task a supervisor can complete in a day

Let w = amount of task a worker can complete in a day 

then

1s + 3w = 1/4

2s + 1w = 1/3

Equation (1) times two

2s + 6w = 1/2

2s + 1w = 1/3

We found that w = 1/30 and s = 3/20.

It means a worker can complete 1/30 of the task in a day.
Hence to complete the entire task, it takes him 30 days.