Question 127714
A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long would it have taken the painter to do the job alone?
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Let x = time required by the painter to do the job alone
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Let the completed job = 1
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Think of of it this way. The painter has 10/x of the job completed when he's joined by the helper
{{{10/x}}} + {{{6/x}}} + {{{6/30}}} = 1
same as:
{{{16/x}}} + {{{6/30}}} = 1
:
Multiply equation by 30x to get rid of the denominator
30x*{{{16/x}}} + 30x*{{{6/30}}} = 30x(1)
:
30(16) + 6x = 30x
480 + 6x = 30x
480 = 30x - 6x
480x = 24x
x = {{{480/24}}}
x = 20 days, painter by himself
:
:
We can check that using the original equation
{{{10/20}}} + {{{6/20}}} + {{{6/30}}} = 
{{{5/10}}} + {{{3/10}}} + {{{2/10}}} = 1