SOLUTION: One computer can process a payroll in 60 minutes. A newer computer can process a payroll in 40 minutes. How long would it take to process the payroll if both computers worked toget

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Question 72718This question is from textbook Algebra:Structure and Method
: One computer can process a payroll in 60 minutes. A newer computer can process a payroll in 40 minutes. How long would it take to process the payroll if both computers worked together? This question is from textbook Algebra:Structure and Method

Found 2 solutions by ankor@dixie-net.com, bucky:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
One computer can process a payroll in 60 minutes. A newer computer can process a payroll in 40 minutes. How long would it take to process the payroll if both computers worked together?
:
Let x = time required when computers work together:
Let the completed job = 1
:
x%2F60+%2B+x%2F40 = 1
:
multiply equation by 120 to get rid of the denominators:
2x + 3x = 120
:
5x = 120
x = 120/5
x = 24 minutes working together
:
Check:
24/60 + 24/40 =
2/5 + 3/5 = 1

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
One way to look at this is that in 1 minute the first computer does 1%2F60 of the job.
.
And in the same time (1 minute) the new computer does 1%2F40 of the job.
.
Stop and think about this a little. It'll help to make sense of this problem. If the first
computer runs for 30 minutes, how much of the job will it complete? Just multiply the 30 minutes
times 1%2F60 and you get 30%2F60 and this reduces to 1%2F2. So if it takes 60
minutes to complete the entire job, in 30 minutes it will be half done. Now think about what
we did to find this out. We multiplied the Rate which is 1%2F60 of the job per each
minute times the number of minutes. The same sort of thinking could be done for the second
(newer) computer. It completes 1%2F40 of the job each minute and by multiplying
this rate by the number of minutes it operates, you can determine how much of the job it
has completed. In the same 30 minutes as the first machine it would do
.
%281%2F40%29%2A30+=+30%2F40+=+3%2F4
.
or three-quarters of the job. Obviously, 30 minutes is too much time because the two machines
working together complete one-half plus three- quarters of the job in 30 minutes or more
than the entire job.
.
So in each case let's multiply the elapsed time by the rate for the computer and when you
add the two computer outputs together it should equal 1 job done. In equation form this
becomes:
.
%281%2F60%29%2At+%2B+%281%2F40%29%2At+=+1
.
where t represents the time from the start when the two computers began working on the job.
.
If you factor the t from the two terms on the left side of this equation you get:
.
t%2A%28%281%2F60%29+%2B+%281%2F40%29%29+=+1
.
A common denominator for the two fractions is 120. 1%2F60+=+2%2F120 and 1%2F40+=+3%2F120
so that when you add these two you get %283%2B2%29%2F120+=+5%2F120%29.
.
The equation then becomes:
.
t%2A%285%2F120%29+=+1
.
You can now solve the equation either by dividing both sides by 5%2F120 or by multiplying
both sides by 120%2F5.
.
When you do that the equation becomes:
.
t+=+%28120%2F5%29
.
and dividing 5 into 120 results in an answer of 24. So 24 minutes is the amount of processing
time it will take both machines working together to do 1 payroll.
.
Hope this helps you to understand the problem a little better.