Question 910353
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