Question 160623

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