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
Algebra.Com
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) (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
:
= 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) (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 of the job.
.
And in the same time (1 minute) the new computer does 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 and you get and this reduces to . 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 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 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
.
.
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:
.
.
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:
.
.
A common denominator for the two fractions is 120. and
so that when you add these two you get .
.
The equation then becomes:
.
.
You can now solve the equation either by dividing both sides by or by multiplying
both sides by .
.
When you do that the equation becomes:
.
.
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.
RELATED QUESTIONS
it takes a computer 30 mins to process and print payroll checks, when a second computer... (answered by jorel555,Boreal)
A computer can process the payroll for Hometel in 13 hours. An older back-up computer... (answered by josgarithmetic)
A new computer can process a company’s monthly payroll in 1 hour less time than the old... (answered by solver91311)
A new computer can process a company’s monthly payroll in 1 hour less time than the old... (answered by ptaylor)
A new computer can process a company's monthly payroll in 1 hour less time than the old... (answered by checkley77)
An old computer can do the weekly payroll in 5 hours. A newer computer can do the same... (answered by Theo)
One computer can process the payroll for a company in 5hours. A new computer can process... (answered by nerdybill)
AT THE NCNB SAVINGS BANK IT TAKES A COMPUTER 4 HOURS TO PROCESS AND PRINT PAYROLL CHECKS. (answered by checkley71)
i am really stuck on this problem can anybody help me, thanks! One computer can process a (answered by Alan3354)