SOLUTION: It takes Jack 9 hours longer to paint the fence than Mike. Together, they can paint the fence in 20 hours. How long will it take each person to paint the fence? I tried solvin

Question 300150: It takes Jack 9 hours longer to paint the fence than Mike. Together, they can paint the fence in 20 hours. How long will it take each person to paint the fence?
I tried solving this as an inverse work-rate problem using
1/A + 1/B = 20 but I can't get it to work.
Found 2 solutions by nerdybill, richwmiller:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
It takes Jack 9 hours longer to paint the fence than Mike. Together, they can paint the fence in 20 hours. How long will it take each person to paint the fence?
.
Let m = hours it takes Mike to paint fence
then
m+9 = hours it takes Jack to paint fence
.
20(1/m + 1/(m+9)) = 1
Multiplying both sides by m(m+9):
20((m+9) + m) = m(m+9)
20(2m+9) = m(m+9)
40m+180 = m^2+9m
0 = m^2-31m-180
0 =(x-36)(x+5)
x = {36, -5}
Throw away the negative solution leaving:
x = 36 hours (Mike)
.
Jack:
x+9 = 45 hours

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
20/x+20/(x+9)=1
The one means one job
We are trying to find what fraction of the job Jack does and what fraction of the job Mike does. Together it has to add up to one whole job or 100% of the job
20/x is how much Mike does in the4 20 hour job
20/(x+9) is the part Jack does since he takes longer.
jack can do it in x+9 hours and so he does 1/(x+9) in one hour.
in 20/(x+9) he does his part of the 20 hour job

so we multiply 20/x by (x+9)/(x+9)
and we multiply 20/(x+9) by x/x
(20*(x+9)+20x)/x*(x+9)=1
(40x+180)=x^2+9x
0=x^2-31x-180
we want factors of -180 that add up to -31
-18 and 10 sum -8
-36 and 5 -31
ok
(x-36)*(x+5)=0
x=36 and x=-5
reject negative
x=36
20/36+20/45=1
5/9+4/9=1
jack take 45 hours alone and mike takes 36 alone
and together they take 20 hours
in 20 hours jack does 4/9 of the job and mike does 5/9

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