SOLUTION: Together John and Michael can paint a wall in 21 minutes. Alone John needs 11 minutes longer to paint the wall than� Michael needs. How much time does� John need to paint the wall

Question 910531: Together John and Michael can paint a wall in 21 minutes. Alone John needs 11 minutes longer to paint the wall than� Michael needs. How much time does� John need to paint the wall by himself? Give your answer to the nearest tenth of a minute.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1/x+1/(x+11)=1/21
(21*x*(x+11))/x+(21*x*(x+11))/(x+11)=(21*x*(x+11))/21
(21*(x+11))+21*x=x*(x+11)
21*x+231+21*x=x^2+11*x
42*x+231=x^2+11*x
x^2-31*x-231=0
Can it be factored?
What factors of -231 add up to -31?
Nevertheless, we will complete the square
x^2-31*x=231
Add it.
x^2-31*x+(-31/2)=231+(-31/2)
Square it.
x^2-31*x+(961/4)=231+(961/4)
x^2-31*x+(240.25)=231+(240.25)
x^2-31*x+(240.25)=471.25
(x-15.5)^2=471.25
(x-15.5)^2=471.25
We will continue.
x+-15.5=(+-)21.7082933
x=15.5(+-)21.7082933
Positive useful answer:
x=15.5+21.7082933
One worker is x=37.2082933 or 37.2 minutes
x+11=11+37.2082933
x+11=48.2082933
Other worker =48.2082933 or 48.2 minutes
check
1/x+1/(x+11)=1/21
1/37.2082933+1/(37.2082933+11)=1/21
1/37.2082933+1/48.2082933=1/21
0.26875729e-1+0.20743319e-1=0.47619048e-1
0.47619048e-1=0.47619048e-1
ok
Useless answer:
x=15.5-21.7082933
Useless answer is x=-6.20829335
x =-6.20829335
This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results

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