SOLUTION: How would I solve this as well as write it out? "A small engineering company has two machines, one which produces 30 components per and another which produces 40 components per

Algebra ->  Rate-of-work-word-problems -> SOLUTION: How would I solve this as well as write it out? "A small engineering company has two machines, one which produces 30 components per and another which produces 40 components per       Log On


   

Question 160623: How would I solve this as well as write it out?
"A small engineering company has two machines, one which produces 30 components per and another which produces 40 components per hour. Both machines were in operation for different periods of time and totaled 15 hours of operation. If 545 components were produced during the total number of hours of operations, determine how many hours each machine was operating."
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let x=number of hours machine 1 is in operation (30 components per hr)
And y=number of hours machine 2 is in operation
And we are told that:
x+y=15-------------------------------eq1
Machine 1 operates at the rate of 30 components per hour
Machine 2 operates at the rate of 40 components per hour
Now we know that:
30x+40y=545 divide each term by 5 just to reduce the size of the numbers and we get:
6x+8y=109------------------------------eq2
multiply eq1 by 6(we get 6x+6y=90) and then subtract it from eq2
2y=19 divide each side by 2
y=9.5 hrs------------------number of hours machine 2 is in operation
Substitute y=9.5 into eq1:
x+9.5=15 subtract 9.5 from each side
x=15-9.5=5.5 hrs------------------number of hours machine 1 is in operation
CK
30*5.5+40*9.5=545
165+380=545
545=545
Hope this helps---ptaylor