Question 249470
The key to solving "job" problems is to realize the job is 1 whole job that is divided into components that people do at different rates.
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One painter paints the house in 6 hours, so his rate is 1/6 of the house per hour.
The other painter takes 9 hrs, so his rate is 1/9 of the house per hour.
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Since we are not told otherwise, we assume they are working simultaneously: we assume they start and stop at the same time.  So each of them works the same amount of time, which we will call  'x' hours.
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First we set up time/rate for both painters:  painter 1 works 'x' hrs at 1/6 of the whole job per hr; painter two works 'x' hrs at 1/9 of the whole job per hr:
{{{x/6 + x/9 = 1}}}
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The least common denominator is 54:
{{{(9x + 6x)/54 = 1}}}
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Cross multiply
{{{15x = 54}}}
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Divide both sides by 15
{{{x = 3.6}}}
Working together it takes them 3.6 hrs to paint the house.
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Check by substituting back into the painter's rates to see if they total 1.
{{{3.6/6 = .6}}}
{{{3.6/9 = .4}}}
So working together they complete 1 whole job in 3.6 hr = 3 hr 36 min = 216 minutes, depending on the units the answer should be in.
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Done.