Question

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? Enter your answer in the box.

Answer 1

I think the answer is 4.5 hours. Equation:  y = 2x + 16.5. 

Where y represents the total area painted by each person and x represents the time.

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 your answer, you can plug the x value into both equations: 2 (4.5) + 16.5 = 25.5 4 (4.5) + 7.5 = 25.5 This proves 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).

Hoped I helped!