SOLUTION: Working together, Angel and Sheila painted a fence in 8 hours. Last year, Sheila painted the fence by herself. the year before, Angel painted it by herself, but it took 12 hours le

Algebra ->  Test -> SOLUTION: Working together, Angel and Sheila painted a fence in 8 hours. Last year, Sheila painted the fence by herself. the year before, Angel painted it by herself, but it took 12 hours le      Log On


   

Question 909877: Working together, Angel and Sheila painted a fence in 8 hours. Last year, Sheila painted the fence by herself. the year before, Angel painted it by herself, but it took 12 hours less than Sheila took. how long did Angel and Sheila take, when each was painting alone?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/(x+12)=1/8
(8*x*(x+12))/x+(8*x*(x+12))/(x+12)=(8*x*(x+12))/8
(8*(x+12))+8*x=x*(x+12)
8*x+96+8*x=x^2+12*x
16*x+96=x^2+12*x
x^2-4*x-96=0
x^2-4*x=96
add it
x^2-4*x+(-4/2)=96+(-4/2)
square it
x^2-4*x+(16/4)=96+(16/4)
x^2-4*x+(4)=96+(4)
x^2-4*x+(4)=100
(x-2)^2=100
(x-2)^2=100
we can continue
x-2=+-10.0
x=2+-10.0
Positive useful answer:
x=2+10.0
One answer is x=12
x+12=12+12
x+12=24
check
1/x+1/(x+12)=1/8
1/12+1/(12+12)=1/8
1/12+1/24=1/8
2/23+1/24=3/24
3/24=3/24
ok
Useless answer:
x=2-10.0
Useless answer is x=-8.0
x =-8.0
This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results