Question

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?

Answer 1

53 hours

Explanation:

If A is the time it takes Company A, and B is the time it takes Company B, then:

1/27 = 1/A + 1/B

A = B + 2

Substitute and solve:

1/27 = 1/(B + 2) + 1/B

1/27 = (B + B + 2) / (B (B + 2))

1/27 = (2B + 2) / (B² + 2B)

27 (2B + 2) = B² + 2B

54B + 54 = B² + 2B

0 = B² − 52B − 54

B = [ -(-52) ± √((-52)² − 4(1)(-54)) ] / 2(1)

B = (52 ± √2920) / 2

B ≈ 53.0

It would take Company B approximately 53 hours.