Question 1038207
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Paul can do a certain job in half the time that Jim requires to do it. 
Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours. 
What length of time, in hours, would Paul, working alone, take to do the whole job?
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Let 'a' be the Jim's rate of work, i.e. part of work, which Jim makes in 1 hour.

Then the Paul's rate of work is 2a, according to the problem.


Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours. 


It means that

    a + 10*(2a) = 1,    where '1' represents the whole job.


From this equation, we find

    a + 20a = 1  --->  21a = 1  --->  a = 1/21.


It means that Jim makes 1/21 of the Job per hour.
In other words, Jim needs 21 hours to make the whole job alone.

Hence, according to the problem, Paul needs half of 21 hours to make the whole job alone.

In other words, Paul needs 21/2 = 10.5 hours to make the whole job alone.    <U>ANSWER</U>
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