Answer:
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.
The time that it would take each worker to do the entire job by himself is; one worker will take 40 days while the other worker will take 60 days.
Let x and y represent the number of days required for each worker to finish the job.
We are told that they each do half of the job and it takes them 50 days.
Thus;
¹/₂x + ¹/₂y = 50 ----(eq 1)
We are told that, if they were working together, they could finish the job in 24 days. Thus, rate = 1/24 and so we can write;
(1/x) + (1/y) = 1/24 -----(eq 2)
We can further simplify this to get;
y + x = xy/24 ----(eq 3)
From, eq 1 we can express as;
y = 100 - x
Thus, putting 100 - x for y in eq 3 to get;
100 - x + x = x(100 - x)/24
⇒ 100 × 24 = 100x - x²
⇒ x² - 100x + 2400
From online quadratic equation solver, we have;
x = 40 or 60
Thus, we can say that one worker will take 40 days while the other worker will take 60 days.
Read more about work rate at; https://brainly.com/question/13186211
