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Naomi and Claire are painting a mural. Naomi paints 2 square feet per hour and has already painted 16.5 square feet.
Claire paints 4 square feet per hour and has already painted 7.5 square feet.
How many more hours will it take for Naomi and Claire to paint an equal total number of square feet?

Respuesta :

W0lf93
4.5 hours We can sum up the information in the question with two equations: y = 2x + 16.5 y = 4x + 7.5 Where y represents the total area painted by each person and x represents the time. These equations are in the form y = mx + b where m is the rate and b is the value at x = 0. To find out when they have painted an equal area, we need to solve for the value of x (time) when the values of y (area) are equal. There's multiple ways to solve systems of equations, but one method is well suited to this particular problem. Subtract one entire equation from the other, as in: y = 2x + 16.5 - y = 4x + 7.5 ---------------------- 0 = -2x + 9 Then solve for x, using basic algebra: 2x = 9 x = 9 / 2 x = 4.5 To check our answer, we can plug the x value into both equations: 2 (4.5) + 16.5 = 25.5 4 (4.5) + 7.5 = 25.5 This confirms that, at 4.5 hours later, both Naomi and Claire will have painted 25.5 square feet each. You could also check the answer by graphing both equations and finding the point where the line meets. You will see that the intersection point is (4.5, 25.5).
ernikhil

[tex]4.5\;\rm hours[/tex] more will it take for Naomi and Claire to paint an equal total number of square feet.

Let [tex]x[/tex] more hours are needed for Naomi and Claire to paint an equal total number of square feet.

According to the question,

Naomi paints [tex]2\; \rm{square\; feet\; per \;hour}[/tex]  and has already painted [tex]16.5\;\rm{ square\; feet}[/tex].

Also,

Claire paints [tex]4\; \rm{square\; feet\; per \;hour}[/tex] and has already painted  [tex]7.5\;\rm{ square\; feet}[/tex].

So, to paint an equal total number of square feet-

[tex]2x+16.5=4x+7.5\\4x-2x=16.5-7.5\\2x=9\\x=4.5\;\rm hours[/tex]

Hence, [tex]4.5\;\rm hours[/tex] more will it take for Naomi and Claire to paint an equal total number of square feet.

Learn more about equations here:

https://brainly.com/question/9585437?referrer=searchResults