algebra

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algebra

Two companies working together can clear a parcel of land in 27 hours.  Working alone, it would take Company A 2 hours longer to clear the land than it would Company B.  How long would it take Company B to clear the parcel of land alone? (Round your answer to the nearest tenth.)
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Re: algebra

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