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Question 910622: Together John and Michael can paint a wall in 29 minutes. Alone John needs 13 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+13)=1/29
(29*x*(x+13))/x+(29*x*(x+13))/(x+13)=(29*x*(x+13))/29
(29*(x+13))+29*x=x*(x+13)
29*x+377+29*x=x^2+13*x
58*x+377=x^2+13*x
x^2-45*x-377=0
Can it be factored?
What factors of -377 add up to -45?
Nevertheless, we will complete the square
x^2-45*x=377
Add it.
x^2-45*x+(-45/2)=377+(-45/2)
Square it.
x^2-45*x+(2025/4)=377+(2025/4)
x^2-45*x+(506.25)=377+(506.25)
x^2-45*x+(506.25)=883.25
(x-22.5)^2=883.25
(x-22.5)^2=883.25
We will continue.
x+-22.5=(+-)29.7195222
x=22.5(+-)29.7195222
Positive useful answer:
x=22.5+29.7195222
One worker is x=52.2195222
x+13=13+52.2195222
x+13=65.2195222
Other worker =65.2195222
check
1/x+1/(x+13)=1/29
1/52.2195222+1/(52.2195222+13)=1/29
1/52.2195222+1/65.2195222=1/29
0.19149926e-1+0.15332832e-1=0.34482759e-1
0.34482759e-1=0.34482759e-1
ok
Useless answer:
x=22.5-29.7195222
Useless answer is x=-7.2195222
x =-7.2195222
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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