SOLUTION: Two companies working together can clear a parcel of land in 13 hours. Working alone, it would take Company A 10 hours longer to clear the land than it would Company B. How long

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Question 1162682: Two companies working together can clear a parcel of land in 13 hours. Working alone, it would take Company A 10 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.
Found 2 solutions by VFBundy, MathTherapy:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Rate (per hour) of Company B working alone = 1%2FB

Rate (per hour) of Company A working alone = 1%2F%28B%2B10%29

Rate (per hour) of both companies working together = 1%2F13 = 1%2FB + 1%2F%28B%2B10%29

Solve for B:

1%2F13 = 1%2FB + 1%2F%28B%2B10%29

1%2F13 = 1%28B%2B10%29%2FB%28B%2B10%29 + 1%28B%29%2FB%28B%2B10%29

1%2F13 = %28B%2B10%29%2F%28B%5E2%2B10B%29%29 + B%2F%28B%5E2%2B10B%29

1%2F13 = %28%28B%2B10%29%2BB%29%2F%28B%5E2%2B10B%29

1%2F13 = %282B%2B10%29%2F%28B%5E2%2B10B%29

1%28B%5E2%2B10B%29 = 13%282B%2B10%29

B%5E2%2B10B = 26B%2B130

B%5E2-16B-130 = 0

B = 8-sqrt%28194%29 = -5.9
B = 8%2Bsqrt%28194%29 = 21.9

You can throw out the negative result, since the rate cannot be a negative number. Therefore, you are left with the result of 21.9.

It takes Company B 21.9 hours to clear the land working alone.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Two companies working together can clear a parcel of land in 13 hours. Working alone, it would take Company A 10 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.
Let time Company B takes, be B

Then time Company A takes = B + 10

We then get: matrix%281%2C3%2C+1%2FB+%2B+1%2F%28B+%2B+10%29%2C+%22=%22%2C+1%2F13%29

             matrix%281%2C3%2C+13%28B+%2B+10%29+%2B+13B%2C+%22=%22%2C+B%28B+%2B+10%29%29 ----- Multiplying by LCD, 13B(B + 10)

             

The above quadratic doesn't have INTEGER roots, so you can use either the quadratic equation formula, or you can

"complete the square" to determine the value of B, the time it takes Company B to complete the entire job.