<PRE><B>Question 102963</B>
Ryan can mow a lawn in 1 hour, and his son, Malik, can mow the same lawn in 50 minutes. One day Malik started mowing the lawn by himself, and worked for 30 minutes. Then Ryan joined him, and they finished the lawn. How long did it take them to finish mowing the lawn, after Ryan started to help?
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Assuming they have two lawn mowers.
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Let x = time required to finish the lawn, together
Let the completed job = 1
:
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M, by himself + the two together = completed job
{{{30/50}}} + {{{x/50}}} + {{{x/60}}} = 1
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Multiply equation by 300 to get rid of the denominators:
300*{{{30/50}}} + 300*{{{x/50}}} + 300*{{{x/60}}} = 300*1
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Cancel out the denominators and you have:
6(30) + 6x + 5x = 300
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180 + 11x = 300
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11x = 300 - 180
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x = 120/11
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x = 10.91 minutes
:
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Check solution on a calc:
{{{3/5}}} + {{{10.91/50}}} + {{{10.91/60}}} =
  .6 + .2182 + .1818  = 1.0000
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