SOLUTION: Painting - You and your friend are painting the walls in your apartment. You estimate that there is 1000 square feet of space to be painted. You paint at a rate of 4 square feet p

Question 159671: Painting - You and your friend are painting the walls in your apartment. You estimate that there is 1000 square feet of space to be painted. You paint at a rate of 4 square feet per minute and your friend paints at a rate of 3 square feet per minute. your friend shows up to help you paint 45 minutes after you have already started painting.
a. Write an equation that gives the total number of square feet y as a function of the number of minutes x it takes to paint all of the walls.
b. How long will it take you and your friend to finish painting?
I was thinking for part a - y=4x + (3x-45) but I don't think that is right.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

In the 45 min that you are painting alone, you are able to paint:
4*45=180 sq ft; this leaves 1000-180=820 sq ft yet to be painted
You and your friend, together, paint at the rate of 4+3=7 sq ft /min
Let x=number of minutes it takes to paint all the walls
Then x-45=number of minutes it takes you and your friend to finish painting
Let y=number of sq ft as a function of the number of minutes it takes to paint all the walls
y=7*(x-45)+4*45 or
y=7x-315+180
y=7x-135 since y=1000, we have
1000=7x-135 add 135 to both sides
7x=1135
x=162.143 min-----total time to paint all the walls
x-45=162.143-45=117.143------------------number of minutes it takes you and your friend to finish painting
CK
Number of minutes it takes you and your friend to finish painting=t
7t=820
t=117.143
Plus the 45 min that you spent painting alone=162.143
Hope this helps---ptaylor

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