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You can put this solution on YOUR website!
Let x = the number of hours the first person takes to do the whole job alone.
\n" ); document.write( "Let y = the number of hours the second person takes to do the whole job alone.
\n" ); document.write( "When they work together it will take them n hours as given by the following formula:
\n" ); document.write( "(1) n = 1/(1/x + 1/y)
\n" ); document.write( "This is a very useful formula to use on this type of problem, put it in your file for future work.
\n" ); document.write( "In your problem we know two facts - just enough to solve for two unknowns, x and y.
\n" ); document.write( "Firstly we know that the total time it takes for the two people working together is 6 hours, therefore
\n" ); document.write( "(2) n = 6
\n" ); document.write( "The second fact is that one of them works twice as fast as the other, so that person takes one half the time as the other. Let's say that x is the faster worker, therefore we have
\n" ); document.write( "(3) x = y/2
\n" ); document.write( "Now put (2) and (3) into (1) to get
\n" ); document.write( "(4) 6 = 1/(2/y + 1/y) or
\n" ); document.write( "(5) 6 = y/(2 + 1) or
\n" ); document.write( "(6) 6 = y/3 or
\n" ); document.write( "(7) y = 18
\n" ); document.write( "So it takes the slower person 18 hours to do the job alone, whereas it only takes the faster person one half of this time or 9 hours.
\n" ); document.write( "Let's check this using the magic formula (1).
\n" ); document.write( "Is (6 = 1/(1/9 + 1/18))?
\n" ); document.write( "Is (6 = 1/(3/18))?
\n" ); document.write( "Is (6 = 18/3)?
\n" ); document.write( "Is (6 = 6)? Yes
\n" ); document.write( "Answer: The faster worker takes 9 hours to do the whole job alone.
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