Two farmers dug the well in 24 hours. How many hours would each of them have

Two farmers dug the well in 24 hours. How many hours would each of them have to work separately if it took one of them 20 hours more to complete the work?

Assuming x is the time it will take for one farmer to complete the work, then:
x + 20 – the time it will take another,
1 / x productivity of the first farmer,
1 / (1 + x) second.
Since 1/24 of their total labor productivity according to the condition of the problem, we obtain the equation:
1 / x + 1 / (x + 20) = 1/24
(x + 20) + x = 1/24 * x (x + 20)
24 (2 * x + 20) = x (x + 20)
48x + 20 = x ^ 2 + 20x
x ^ 2-28 * x-20 = 0
x12 = (28 + -√784-4 * (- 20)) / 2 = (28 + -30) / 2
x = 58/2 = 29 hours; the second root of the equation is meaningless.
Another Farmer’s Time:
20 + 29 = 49 hours.