1
$\begingroup$

A factory is currently running at $85\%$ of its original capacity, and management is considering upgrading the equipment. The upgrade will take $6$ months, during which time the factory will not run at all. Once complete, the factory’s output will increase to $120\%$ of the original capacity.

After how long would the upgraded factory’s production match the current $85\%$ production? In other words, how long will it take for the factory to make up for the loss of $6$ months?

This what I have come up with so far:

$0.85E - 6m = 100$ and $1.20E + 6m = m$

$E$ represents the percentage capacity, $m$ represents the months, and $100$ represents the factory original output of $100$ units per month.

I understand how to solve using system of equations but I am having difficult with coming up with a set of equations for this problem in particular.

$\endgroup$
1
$\begingroup$

So after 6 months, with the new equipment, the factory will produce at 120 units per month, which is 120-85 = 35 units better, so how long does it take for 35 units more a month to be worth 6 months at 85 units?

$$6*85 = 35 * t$$

$$t = 510/35 = 14.571$$

So after 1 year and 3 months will have completely recovered its losses

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.