Mike and David are each assigned to produce x identical widgets. Based on their respective rates, Dave calculates that it will take him 5 hours to produce the widgets while Mike calculates that it will take him 2 hours longer than Dave. Dave agrees to make Y of Mikes widgets so that they can each complete the task in the same amount of time. What is the number of widgets, interms of y, that Mike was assigned to make?
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Here: each is assigned x widgets to make, and Dave takes y away from Mike's load, so Dave makes x + y and Mike must make x - y.
(amount) = (rate)(time) ====> A = RT
Dave's rate = amount/time = x/5
Mike's rate = x/7
For Dave: A = RT ---> x+y = (x/5)*T ---> 5(x+y)/x = T
For Mike: A = RT ---> x-y = (x/7)*T ---> 7(x-y)/x = T
Both T's are equal, so set these equations equal:
5(x+y)/x = 7(x-y)/x ---- then multiply by x --->
5(x+y) = 7(x-y) ---- then distribute --->
5x + 5y = 7x - 7y --- then combine terms --->
12y = 2x
We want to solve for "the number of widgets ... that Mike was assigned to make
" = x, in terms of y. Divide by 2.
6y = x
So, the number of widgets each was assigned to make, x, is equal to 6y.
Does that make sense?
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