SOLUTION: Betty and Frank, working together can paint the exterior of a house in 3 days. Frank, by himself can complete the job in 8 days less than Betty. How long will it take Betty to comp

Question 116908: Betty and Frank, working together can paint the exterior of a house in 3 days. Frank, by himself can complete the job in 8 days less than Betty. How long will it take Betty to complete the job by herself?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Betty can paint a house in b days.
Frank can paint a house in (b-8) days.
.
1/b is the amt of the job betty can do in 1 day.
1/(b-8) is the amt of the job Frank can do in 1 day.
.
1/b+ 1/(b-8)=1/3
3(b-8)+3b=b(b-8) Multiply each side by 3b(b-8) to eliminate fractions.
3b-24+3b=b^2-8b
b^2-14b+24=0
(b-2)(b-12)=0
b=2, b=12 since Frank can do the job 8 days sooner than Betty b=2 is not an answer.
b=12 days, f=4 days
Check:
1/12+ 1/4 =1/3
1/12+ 3/12= 4/12 True.
.
Ed

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