Two spray paint machines are used to paint different portions of a large wall. The first machine (nicknamed "Paint Pro") is used for two hours. The second machine (nicknamed "Goldilocks") is used for an hour and a half. When they are working at the same time, they can paint 55 square feet per minute. Together they painted 5850 square feet of wall. How many square feet of wall per minute can each machine paint?

Paint Pro can paint 30 square feet of wall per minute while Goldilocks can paint 25 square feet of wall per minute.

Step-by-step explanation

Let

x = portion of the wall painted by Paint Pro

y = portion of the wall painted by Goldilocks

Together, they can paint 55 square feet per minute. Therefore:

?x+y=55?

Now, we multiply the number of hours each machine was used in total and equate this to the total number of area painted. Paint Pro was used for 120 minutes (2 hours) while Goldilocks was used for 90 minutes (1 and a half hour). Therefore, our equation becomes:

?120x+90y=5850?

Now we have a system of linear equations:

?x+y=55?

?120x+90y=5850?

By substitution, we can express y in terms of x in the first equation and substitute this into the second equation:

?y=55−x?

?120x+90(55−x)=5850?

?120x+4950−90x=5850?

?30x=900?

?x=30?

We substitute back the obtained value of x into the expression for y:

?y=55−x?

?y=55−30?

?y=25?

Therefore, Paint Pro can paint 30 square feet of wall per minute while Goldilocks can paint 25 square feet of wall per minute.