Question 115432
Working alone Shana can rake the leaves in the yard in 4-1/2 hrs, while it takes John only 3 hrs to do the same task. How fast can they rake the leaves if they work together if they both work at their original rates?
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Let x = time required to complete the job when they work together
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Let the completed job = 1
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A simple equation
{{{x/4.5}}} + {{{x/3}}} = 1
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We can get rid of the denominators by multiplying by 9
9*{{{x/4.5}}} + 9*{{{x/3}}} = 9(1)
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Cancel out the denominators and you have:
2x + 3x = 9
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5x = 9
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x = {{{9/5}}}
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x = 1.8 hrs working together:
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Check solution using the original equation:
{{{1.8/4.5}}} + {{{1.8/3}}} = 
   .4 + .6 = 1