document.write( "Question 243807: The Epson Stylus 850 can print Helen's class project in 18 minutes. The Epson Stylus 500 can print the project in 36 minutes. If the two printers work together, how long would they take to print out the project? \n" ); document.write( "

Algebra.Com's Answer #854114 by greenestamps(13326) $\"\"$ $\"About$

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\n" ); document.write( "The response from tutor @MathTherapy shows the standard formal algebraic method for solving \"working together\" problems like this.

\n" ); document.write( "Here are two (very similar) less formal methods for solving such problems, if a formal algebraic solution is not required.

\n" ); document.write( "(1) Notice that the model 850 can do the job in half the time required by the model 500. That means the model 850 does work twice as fast as model 500, so it is like having two model 500s working together. So one model 850 and one model 500 is like have 2+1 = 3 model 500s. And since one model 500 can print the job in 36 minutes, 3 model 500s can print the job in 36/3 = 12 minutes.

\n" ); document.write( "ANSWER: 12 minutes

\n" ); document.write( "(2) Consider the least common multiple of the two given times; the least common multiple of 18 and 36 is 36.

\n" ); document.write( "Consider what the two model could do in 36 minutes. The model 500 in 36 minutes could do the job 36/36 = 1 time; the model 850 in 36 minutes could do the job 36/18 = 2 times. So the two models together in 36 minutes could do the job 1+2 = 3 times; therefore, they could do the one job together ins 36/3 = 12 minutes.

\n" ); document.write( "ANSWER: 12 minutes

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