SOLUTION: Two companies working together can clear a parcel of land in 26 hours. Working alone, it would take Company A 2 hours longer to clear the land than it would Company B. How long wou

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Question 1190530: Two companies working together can clear a parcel of land in 26 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.)
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

x = time it takes for Company B to get the job done alone
x+2 = time it takes for Company A to get the job done alone
Time values are in hours

It takes x hours for company B to do the job alone
The unit rate is 1/x jobs per hour
The unit rate for company A is 1/(x+2) for similar reasoning.

Add up the two unit rates
1%2Fx+%2B+1%2F%28x%2B2%29

%28x%2B2%29%2F%28x%28x%2B2%29%29+%2B+x%2F%28x%28x%2B2%29%29

%28x%2B2%2B+x%29%2F%28x%28x%2B2%29%29

%282x%2B2%29%2F%28x%28x%2B2%29%29
This is the combined unit rate of the two companies.

Now I'll use this idea
(work rate)*(time) = amount done

The idea is that we multiply the combined unit rate we found by the 26 hours it takes for both companies to work together.
This should result in 1 to represent 1 full job completed.

%28%282x%2B2%29%2F%28x%28x%2B2%29%29%29%2A26+=+1

%2826%282x%2B2%29%29%2F%28x%28x%2B2%29%29+=+1

%2852x%2B52%29%2F%28x%5E2%2B2x%29+=+1

52x%2B52+=+x%5E2%2B2x

0+=+x%5E2%2B2x-52x-52

x%5E2-50x-52+=+0

Then we use the quadratic formula
Use a = 1, b = -50, c = -52
x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%28-50%29%2B-sqrt%28%28-50%29%5E2-4%281%29%28-52%29%29%29%2F%282%281%29%29

x+=+%2850%2B-sqrt%282708%29%29%2F%282%29

x+=+51.019 or x+=+-1.019 both are approximate

Ignore the negative x value, since negative time values aren't allowed.

Answer: Approximately 51.0 hours