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?
Found 3 solutions by devinbrowning93, MathTherapy, greenestamps:
Answer by devinbrowning93(1)   (Show Source):
You can put this solution on YOUR website! im no tutor but i believe you add the two times together 36+18=44
and divide it by 2 this is not definite im just trying to help a fellow student in need
Answer by MathTherapy(10801)  (Show Source):
You can put this solution on YOUR website!
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?
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At least this person admitted that he/she is NOT a tutor, and is omly trying to help. But, instead of engaging in a task that
might be too much for him/her, why NOT just leave the problem alone, so someone who knows how to solve it, can do so?
Needless to say, this person's answer is WRONG. 18 is NOT added to 36, and then the result is divided by 2 to get 22 hours.
This makes absolutely NO SENSE!
One should realize that, since 1 printer can do the job (print the project) in 18 minutes, it's IMPOSSIBLE for both printers,
working together, to do the same job (print the project) in more time than it takes 1 printer, working alone. With both
working together, it will MOST DEFINITELY take less time than it takes just 1 to print the project. Makes sense?
Anyway, let the time it takes both printers to print the project, be T
The FASTER printer, working alone, takes 18 minutes to print the project, or can do  of the job in 1 minute
Likewise, the SLOWER printer, working alone, takes 36 minutes to print the project, or can do  of the job in 1 minute
We then get the following TOTAL-JOB equation: 
2T + T = 36 ---- Multiplying by LCD, 36T
3T = 36
Time it takes both printers, working together, to do the job, or 
Do you notice that the model numbers: Epson Stylus 850 and Epson Stylus 500 were included? Including IRRELEVANT numbers,
is DELIBERATELY done, at times, to confuse the reader.
Answer by greenestamps(13326)  (Show Source):
You can put this solution on YOUR website!
The response from tutor @MathTherapy shows the standard formal algebraic method for solving "working together" problems like this.
Here are two (very similar) less formal methods for solving such problems, if a formal algebraic solution is not required.
(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.
ANSWER: 12 minutes
(2) Consider the least common multiple of the two given times; the least common multiple of 18 and 36 is 36.
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.
ANSWER: 12 minutes
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