document.write( "Question 1038207: 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? \n" ); document.write( "

Algebra.Com's Answer #853844 by n2(55) $\"\"$ $\"About$

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\n" ); document.write( "Paul can do a certain job in half the time that Jim requires to do it.
\n" ); document.write( "Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours.
\n" ); document.write( "What length of time, in hours, would Paul, working alone, take to do the whole job?
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document.write( "Let 'a' be the Jim's rate of work, i.e. part of work, which Jim makes in 1 hour.\r\n" );
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document.write( "Then the Paul's rate of work is 2a, according to the problem.\r\n" );
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document.write( "Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours. \r\n" );
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document.write( "It means that\r\n" );
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document.write( "    a + 10*(2a) = 1,    where '1' represents the whole job.\r\n" );
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document.write( "From this equation, we find\r\n" );
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document.write( "    a + 20a = 1  --->  21a = 1  --->  a = 1/21.\r\n" );
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document.write( "It means that Jim makes 1/21 of the Job per hour.\r\n" );
document.write( "In other words, Jim needs 21 hours to make the whole job alone.\r\n" );
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document.write( "Hence, according to the problem, Paul needs half of 21 hours to make the whole job alone.\r\n" );
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document.write( "In other words, Paul needs 21/2 = 10.5 hours to make the whole job alone.    ANSWER\r\n" );
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