Question 1161400
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Let x be the number of hours the new machine was in operation.

Then the old machine was  (15-x) hours in operation.


Your basic equation is

    30*(15-x) + 40x = 545.


From the equation,

    x = {{{(545-30*15)/(40-30)}}} = 9.5   hours.


<U>ANSWER</U>.  The new machine was 9.5 hours in operation;  the old machine  (15-9.5) = 5.5 hours.


<U>CHECK</U>.  30*5.5 + 40*9.5 = 545 components.    ! Precisely correct !
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Solved.