SOLUTION: Will can paint six rooms in 12 hours working alone If his friend Matthew helps him together they can paint the six rooms in 7 hours How long would it take Matthew to paint the 6 ro

Question 719994: Will can paint six rooms in 12 hours working alone If his friend Matthew helps him together they can paint the six rooms in 7 hours How long would it take Matthew to paint the 6 rooms by himself?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Will can paint six rooms in 12 hours working alone If his friend Matthew helps him together they can paint the six rooms in 7 hours How long would it take Matthew to paint the 6 rooms by himself?
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Will rate: 1/12 job/hr
Together rate: 1/7 job/hr
Matt rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/12 + 1/x = 1/7
------
7x + 84 = 12x
5x = 84
x = 16.8 hrs = 16 hr 48 minutes (time for Matt to do the job alone)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The problem only talks about 6 rooms, so
I can call painting 6 rooms 1 job
Let = the time in hrs for Matthew to
do 1 job by himself
Add their rates of painting to get their rate
painting together
( 1 job ) /( 12 hrs ) + ( 1 job ) / ( t hrs ) = ( 1 job ) / ( 7 hrs )

Multiply both sides by

matthew can do the job in 16.8 hrs by himself
check answer:

close enough

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