document.write( "Question 658831: if A can do the work in \"x\" days and B in \"y\" days, how long will they finish the job working together? \n" ); document.write( "
Algebra.Com's Answer #410487 by Theo(13342)\"\" \"About 
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A does the work in x days.
\n" ); document.write( "B does the work in y days.\r
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\n" ); document.write( "\n" ); document.write( "the basic formula is R*T = 1 where 1 represents the job that has to be done.
\n" ); document.write( "T for worker A is equal to x days.
\n" ); document.write( "T for worker B is equal to y days.\r
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\n" ); document.write( "\n" ); document.write( "formula for worker A is:
\n" ); document.write( "R.1*x = 1
\n" ); document.write( "formula for worker B is:
\n" ); document.write( "R.1*y = 1\r
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\n" ); document.write( "\n" ); document.write( "For worker 1, R.1 is equal to 1/x.
\n" ); document.write( "For worker 2, R.2 is equal to 1/y\r
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\n" ); document.write( "\n" ); document.write( "When they work together their rates are additive.
\n" ); document.write( "This means that the basic formula becomes:
\n" ); document.write( "(R.1 + R.2)*T = 1
\n" ); document.write( "R.1 is the rate for worker 1.
\n" ); document.write( "R.2 is the rate for worker 2.
\n" ); document.write( "T is the overall time it takes to do the job in days.\r
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\n" ); document.write( "\n" ); document.write( "Since R.1 = 1/x and R.2 = 1/y, then the formula becomes:
\n" ); document.write( "(1/x + 1/y) * T = 1
\n" ); document.write( "if we solve for T, we get:
\n" ); document.write( "T = 1 / (1/x + 1/y)\r
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\n" ); document.write( "\n" ); document.write( "That's the general formula.
\n" ); document.write( "to see if the general formula works, then let's try some real numbers.\r
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\n" ); document.write( "\n" ); document.write( "Worker 1 can do the in 5 days.
\n" ); document.write( "Worker 2 can do the job in 10 days.
\n" ); document.write( "The time required to do the job together would then be equal to 1 / (1/5 + 1/10).
\n" ); document.write( "simplify this equation to get:
\n" ); document.write( "T = 1 / (3/10)
\n" ); document.write( "solve for T to get:
\n" ); document.write( "T = 10/3 days.\r
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\n" ); document.write( "\n" ); document.write( "let's see if that's true.\r
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\n" ); document.write( "\n" ); document.write( "worker 1 can do 1/5 of the job in 1 day because it takes him 5 days to do the job alone.
\n" ); document.write( "worker 2 can do 1/10 of the job in 10 days because it takes him 10 days to do the job alone.\r
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\n" ); document.write( "\n" ); document.write( "in 10/3 days, worker 1 can do 1/5 * 10/3 = 10/15 of the job.
\n" ); document.write( "in 10/3 days, worker 2 can do 1/10 * 10/3 = 1/3 of the job.
\n" ); document.write( "since 1/3 of the job is equivalent to 5/15 of the job, then we get:
\n" ); document.write( "worker 1 finishes 10/15 of the job in 10/3 days and worker 2 finishes 5/15 of the job in 10/3 days.
\n" ); document.write( "together they have completed 10/15 + 5/15 of the job which is equal to the whole job.\r
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\n" ); document.write( "\n" ); document.write( "the formula works.
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