SOLUTION: working together john and bob can paint a house in 3 1/2 hours. working alone bob can do the job in 6 hours. how long does it take for john to do the job alone?

Question 965418: working together john and bob can paint a house in 3 1/2 hours. working alone bob can do the job in 6 hours. how long does it take for john to do the job alone?
Found 2 solutions by lwsshak3, macston:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
working together john and bob can paint a house in 3 1/2 hours. working alone bob can do the job in 6 hours. how long does it take for john to do the job alone?
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let x=hours john can do the job alone
1/x=his work rate
1/6=bob's work rate
1/3.5=work rate working together
sum of indv. work rates=work rate working together
..
1/x+1/6=1/3.5
1/x=1/3.5-1/6
lcd:6*3.5*x=21x
21=6x-3.5x
2.5x=21
x=8.4
how long does it take for john to do the job alone? 8.4 hrs
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Bob paints 1 house in 6 hours or 1house/6hrs=1/6 house/hr=1.67 house/hr
In 3.5 hours he paints (3.5hrs)(1.67 house/hr)=0.583 house, so in 3.5 hours,
John painted the rest or 1-0.583=0.417 of the house.
So John paints (0.417 house)/3.5 hours=0.119 house/hr and to paint the whole house:
(1 house)/(0.119 house/hr)=8.4 hours
ANSWER: It would take John 8.4 hours to paint the house alone.
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