document.write( "Question 1099897: Working together, it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 30 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? \n" ); document.write( "

Algebra.Com's Answer #714389 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The traditional algebraic method for solving this kind of problem is to work with the fraction of the job each computer does in a minute.

\n" ); document.write( "let x = number of minutes the faster computer takes to do the job
\n" ); document.write( "then 1/x = the fraction of the job the faster computer does in 1 minute

\n" ); document.write( "The slower computer does the job alone in 30 minutes; so in 1 minute it does 1/30 of the job.
\n" ); document.write( "Working together, the two do the job in 10 minutes; so in 1 minute the two together do 1/10 of the job. Then
\n" ); document.write( " $\"1%2F30+%2B+1%2Fx+=+1%2F10\"$

\n" ); document.write( "... and you can solve the problem from there.

\n" ); document.write( "But here is an alternative method for solving this kind of problem, which usually (as in this case) gets you to the answer much faster.

\n" ); document.write( "Consider the 30 minutes the slower computer takes to do the job alone.
\n" ); document.write( "Since the two computers together can do the job in 10 minutes, in 30 minutes they could complete 3 of the jobs.
\n" ); document.write( "But in those 30 minutes the slower computer is only doing one job; that means the faster computer must be doing the other two jobs.
\n" ); document.write( "So the faster computer can do the job twice in 30 minutes; that means it can do the job once in 15 minutes.

\n" ); document.write( "You should of course get that same answer if you finish solving the problem by the traditional algebraic method above. \n" ); document.write( "

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