A pen factory produces pens at a rate of 18 pens per minute. A competing factory produces pens at a rate of 16 pens per minute but has 4000 pens already produced. After how many minutes will the two pen factories have an equal number of pens?
To find out after how many minutes the two pen factories will have an equal number of pens, we need to set up an equation based on their respective production rates and the initial number of pens produced by the competing factory.
Let's use "x" to represent the number of minutes it takes for the two factories to have an equal number of pens.
The first factory produces pens at a rate of 18 pens per minute, so after "x" minutes, it would have produced 18x pens.
The competing factory already has 4000 pens produced and produces pens at a rate of 16 pens per minute. Therefore, after "x" minutes, it would have produced 16x pens in addition to the initial 4000 pens.
Since we want to find the point at which the two factories have an equal number of pens, we can set up the equation:
18x = 16x + 4000
Now, let's solve this equation for "x":
18x - 16x = 4000
2x = 4000
x = 4000 / 2
x = 2000
After 2000 minutes, both factories will have an equal number of pens.