Two workers, if they were working together, could finish a certain job in 24 days. If one of the workers does the first half of the job and then the other one does the second half, the job will take them 50 days. How long would it take each worker to do the entire job by himself?

Step-by-step explanation:

Setup

Let x and y represent the number of days required for each worker to do the job. Then the time required for each to do half the job will be ...

  x/2 + y/2 = 50

The rate at which the job gets done when they work together is ...

  1/x + 1/y = 1/24 . . . . . . . jobs per day

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Solution

Multiplying the second equation by xy, we have ...

  y + x = xy/24

Multiplying the first equation by 2 and subtracting x, we have ...

  y = 100 -x

  100 -x +x = x(100 -x)/24

  2400 = 100x -x^2 . . . . . multiply by 24

  x^2 -100x +2400 = 0 . . put in standard form

  (x -40)(x -60) = 0 . . . . . . factor

Values of x that make this true are x=40 and x=60. If x is one of these values, y is the other one.

One worker can do the whole job in 40 days; the other worker can do it in 60 days.