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Question 1106092: Paul can do a certain job in half the time that Jim requires to do it. Jim orked alone for an hour and stopped, then Paul complete d the job in 10 hours. What length of time, in hours, woul d Paul, working alone, take to do the whole job?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39790)   (Show Source):
You can put this solution on YOUR website! x, time for Paul working alone to do the job
2x, time for Jim to do the job working alone
ONE job to be done,
 ----------solve this for x.
Answer by ikleyn(53742)  (Show Source):
You can put this solution on YOUR website! .
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. ANSWER
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