Question 121892
Two harvesting machines can each harvest a field in 15 hrs. If they are joined by a newer machine and the three machines work together, the job takes 3 hrs. How long would it take for the newer machine to harvest the field alone?
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Let x = the time the newer machine needs to complete the job alone
Let the completed job = 1
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Each machine will do a fraction of the work
All three will work for 3 hrs so we can say:
Each original machine will 3/15
The new machine: 3/x 
Remember the completed job = 1:
:
{{{3/15}}} + {{{3/15}}} + {{{3/x}}} = 1
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we can simplify this the 1st two machine = 6/15 reduced to 2/5
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Now we have a real simple equation:
{{{2/5}}} + {{{3/x}}} = 1
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Multiply the equation by 5x to get rid of the denominators
5x*{{{2/5}}} + 5x{{{3/x}}} = 5x(1)
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Cancel out the denominators and we have:
2x + 15 = 5x
15 = 5x = 2x
15 = 3x
x = {{{15/3}}}
x = 5 hrs for the new machine to do it alone.
:
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Check solution in the original equation
3/15 + 3/15 + 3/5 =
1/5 + 1/5 + 3/5 = 1; confirms our solution
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Hopefully this provided a few clues, did it make sense to you? Any questions?