Question

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?e 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?

Answer 1

Answer: The answer is 30 sq.ft/min and 25 sq.ft/min.

Step-by-step explanation:  Given that there are two spray paint machines. The first machine (nicknamed "Paint Pro") is used for two hours and 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 and together they painted 5850 square feet of wall.

Let 'x' and 'y' sq.ft/min be the portion of the wall painted by Paint Pro and Goldilocks respectively.

Then, according to the question, we have

$x+y=55,\\\\120x+90y=5850~~\Rightarrow 4x+3y=195.$

Multiplying first equation by 4 and subtracting the second equation from it, we have

$4y-3y=220-195\\\\\Rightarrow y=25,$

and

$x=55-25=30.$

Thus, Paint Pro will paint 30 sq.feet per minute and Goldilocks will paint 25 sq.ft per minute.