x = time for company B working alone

x + 2 = time for company A working alone

1/x = company B work rate

1/(x + 2) = company A work rate

1/x + 1/(x + 2) = 1/27 ← sum of rates equals rates together

27(x + 2) + 27x = x(x + 2) ← multiplied by x(x + 2)

27x + 54 + 27x = x² + 2x ← multiplied by common denominator, 27x(x + 2)

54x + 54 = x² + 2x ← combined terms

x² - 52x -54=0 ← grouped to one side

x ≈ 53.02 hours

- Proof

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