Question 747352: Lisa,an experienced shipping clerk, can fill a certain order in 6 hours. Felipe, a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order?
Answer by mikeebsc(26)   (Show Source):
You can put this solution on YOUR website! At first glance, I realized I solved this problem wrong. The time is not the main factor, it is the RATE which me must look at and solve with. I apologize, it happens:/...especially after working on harder problems, sometimes we oversimplify those that we perceive to be easy. My revision is:
Lisa
time = 6 hr/job ; RATE = 1/6 job/hr (the rate is the reciprocal)
Felipe
time = 11 hr/job ; RATE = 1/11 job/hr (the rate is the reciprocal)
Lisa and Felipe
time = x hr/job ; COMBINED RATE = 1/x job/hr So:
Equation:
Lisa rate + Felipe rate = combined rate
1/6 + 1/11 = 1/x
Multiply 66x(the Least Common Multiple)through: (66x)1/6 + 66x(1/11) = 66x(1/x) which is
66x/6 + 66x/11 = 66x/x then reduce:
11x + 6x = 66
17x = 66 ; now divide both sides by 17 to get x alone:
x = 66/17 ; now do the simple math:
x = 3.88 Hours for Lisa and Felipe to fill the order
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