SOLUTION: Together John and Michael can paint a wall in 23 minutes. Alone John needs 15 minutes longer to paint the wall than Michael needs. How much time does John need to paint the wall by

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Together John and Michael can paint a wall in 23 minutes. Alone John needs 15 minutes longer to paint the wall than Michael needs. How much time does John need to paint the wall by      Log On


   

Question 910120: Together John and Michael can paint a wall in 23 minutes. Alone John needs 15 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) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/(x+15)=1/23
(23*x*(x+15))/x+(23*x*(x+15))/(x+15)=(23*x*(x+15))/23
(23*(x+15))+23*x=x*(x+15)
23*x+345+23*x=x^2+15*x
46*x+345=x^2+15*x
x^2-31*x-345=0
We will complete the square
x^2-31*x=345
add it
x^2-31*x+(-31/2)=345+(-31/2)
square it
x^2-31*x+(961/4)=345+(961/4)
x^2-31*x+(240.25)=345+(240.25)
x^2-31*x+(240.25)=585.25
(x-15.5)^2=585.25
(x-15.5)^2=585.25
we can continue
x-15.5=+-24.1919408
x=15.5+-24.1919408
Positive useful answer:
x=15.5+24.1919408
One answer is x=39.6919408
rounded
x=39.7
x+15=15+39.7
x+15=54.7
Useless answer:
x=15.5-24.1919408
Useless answer is x=-8.69194081
x =-8.69194081
This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results