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Question 910353: Together John and Michael can paint a wall in 31 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)=1/31
(31*x*(x+11))/x+(31*x*(x+11))/(x+11)=(31*x*(x+11))/31
(31*(x+11))+31*x=x*(x+11)
31*x+341+31*x=x^2+11*x
62*x+341=x^2+11*x
x^2-51*x-341=0
Can it be factored?
What factors of -341 add up to -51?
Nevertheless, we will complete the square
x^2-51*x=341
Add it.
x^2-51*x+(-51/2)=341+(-51/2)
Square it.
x^2-51*x+(2601/4)=341+(2601/4)
x^2-51*x+(650.25)=341+(650.25)
x^2-51*x+(650.25)=991.25
(x-25.5)^2=991.25
(x-25.5)^2=991.25
We will continue.
x+-25.5=(+-)31.484123
x=25.5(+-)31.484123
Positive useful answer:
x=25.5+31.484123
One worker is x=56.984123 Michael rounded 57
x+11=11+56.984123
x+11=67.984123
Other worker =67.984123 John rounded 68
check
1/x+1/(x+11)=1/31
1/56.984123+1/(56.984123+11)=1/31
1/56.984123+1/67.984123=1/31
0.17548748e-1+0.14709317e-1=0.32258065e-1
0.32258065e-1=0.32258065e-1
ok
Useless answer:
x=25.5-31.484123
Useless answer is x=-5.98412298
x =-5.98412298
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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