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(3817) (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
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.
Then we use the quadratic formula
Use a = 1, b = -50, c = -52
or both are approximate
Ignore the negative x value, since negative time values aren't allowed.
Answer: Approximately 51.0 hours
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