SOLUTION: Hannah can clear a lot in 5.5 hours. Damon can do the same job in 7.5 hours. How long will it take for them to clear the lot if they work together?

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Question 595771: Hannah can clear a lot in 5.5 hours. Damon can do the same job in 7.5 hours. How long will it take for them to clear the lot if they work together?
Found 2 solutions by scott8148, jerryguo41:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
they each do a FRACTION of the task based on their individual rates; the fractions sum to one, the WHOLE task

(x / 5.5) + (x / 7.5) = 1

Answer by jerryguo41(197) About Me  (Show Source):
You can put this solution on YOUR website!
rH=5.5
rD=7.5
x= number of hours
%28x%2F5.5%29%2B%28x%2F7.5%29=1
%28x%2F%2811%2F2%29%29%2B%28x%2F%2815%2F2%29%29=1
ex. x%2F%281%2F2%29 = 2x
%28%282%2F11%29x%29%2B%28%282%2F15%29x%29=1
Find Common Denominator
%28%2830%2F165%29x%29%2B%28%2822%2F165%29x%29=1
%2852%2F165%29x=1
52x=165}
x=165%2F52
or
x=3.17 hours or 3hours and 10min