
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
