Question 1038207
Jim worked alone for {{{1}}} hour and stopped.
Paul comes in, sees the work Jim did in {{{1}}} hour and says
"It would have taken me {{{1/2}}} to do that. I do any job in half the time it takes Paul to do it"
After Paul worked another {{{10}}} hours, the job was finished.
Then Jim said "SEE!, I could have done the whole thing in {{{10+1/2=highlight(10.5)}}} hours. I may only have a fourth-grade education, but I can work twice as fast as Paul, without knowing what algebra is about."
 
The problem with mananth solution seems to be that after getting to
((x-1)/x)/(2/x)=10 or {{{((x-1)/x)/(2/x)=10}}} mananth apparently thought
"I could simplify the left side expression by writing it as  {{{((x-1)/x)(x/2)}}} because dividing by {{{2/x}}} is multiplying times {{{x/2}}} to end with {{{(x-1)/x}}} on the left and a simple expression on the right.
or I could simplify the equation by multiplying both sides by {{{2/x}}}"
Then mananth had one of those brain-farts and multiplied the left hand side times {{{2/x}}} and the right hand side times {{{x/2}}} ending with {{{(x-1)/x}}} on the left and {{{10(x/2)=5x}}} on the right.
Keeping the equal sign in between, mananth concluded that Jim could have done the whole job in 2 hours, forgetting that it took Jim 10 hours to do part of the job.
We we all have one of those brain farts now and then. One professor told about answering a problem on a radio station show by saying that the top of an 8 foot ladder leaning again the side of a house would be 10 feet above the ground.