SOLUTION: 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 fa

Algebra.Com
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?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!





-
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


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.

let x = number of minutes the faster computer takes to do the job
then 1/x = the fraction of the job the faster computer does in 1 minute

The slower computer does the job alone in 30 minutes; so in 1 minute it does 1/30 of the job.
Working together, the two do the job in 10 minutes; so in 1 minute the two together do 1/10 of the job. Then


... and you can solve the problem from there.

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.

Consider the 30 minutes the slower computer takes to do the job alone.
Since the two computers together can do the job in 10 minutes, in 30 minutes they could complete 3 of the jobs.
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.
So the faster computer can do the job twice in 30 minutes; that means it can do the job once in 15 minutes.

You should of course get that same answer if you finish solving the problem by the traditional algebraic method above.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
There is entire bunch of lessons in this site on joint work problems:
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Using quadratic equations to solve word problems on joint work
    - Solving rate of work problem by reducing to a system of linear equations
    - Selected joint-work word problems from the archive
    - Joint-work problems for 3 participants
    - Had there were more workers, the job would be completed sooner
    - One unusual joint work problem
    - Special joint work problems that admit and require an alternative solution method
    - Joint work word problem for the day of April, 1
    - OVERVIEW of lessons on rate-of-work problems

Read them and get be trained (and get be an expert) in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


---------------------
Regarding the given problem in the post, the solution is THIS: 

The rate of work of two computers working together is   of the job per minute.


The rate of work of the slower computer is  of the job per hour.


Hence, the rate of work of the faster computer is the difference   -  =  =  =  of the job per hour.


It means that the faster computer can complete the job in 15 minutes working alone.

Solved. 
 
     When solving problems like this one, you should know and should remember two basic facts:

         - the rate of work of two workers/machines/tubes  is the sum of the rates of individuals;

         - If you are given the combined rate of work of two workers/machines/tubes and the rate of work of one individual, 
           then the rate of work of the other individual is the difference of rates.

Completely self-evident facts.



RELATED QUESTIONS

Working together, it takes two computers 10 minutes to send out a company’s email. If it (answered by mananth)
It takes an older computer 4 times as long to send out a company’s email as it does a... (answered by stanbon)
Working together, it takes two computers 10 minutes to send out a company’s email. If... (answered by Boreal,greenestamps)
Working together, it takes two computers minutes to send out a company’s email. If it... (answered by Alan3354)
Working together, it takes two computers 15 minutes to send out a company’s email. If it... (answered by nerdybill)
Working together, it takes two computers ??? minutes to send out a company’s email. If it (answered by richwmiller)
It takes an older computer twice as long to send out a company’s email as it does a newer (answered by solver91311)
It takes an older computer 4 times as long to send out a company’s email as it does a... (answered by richwmiller)
It takes an older computer times as long to send out a company’s email as it does a... (answered by richwmiller)