melinda and paula shovel driveways and sidewalks in the winter as a way to earn extra money. together they…

melinda and paula shovel driveways and sidewalks in the winter as a way to earn extra money. together they shoveled 450 square feet of sidewalk in 30 minutes. then melinda shoveled for 20 minutes while paula shoveled for 25 minutes to complete 345 square feet of driveway.\n30x + 30y = 450\n20x + 25y = 345\nhow much more can paula shovel in 1 minute than melinda?\n3 square feet per minute\n6 square feet per minute\n9 square feet per minute\n15 square feet per minute

melinda and paula shovel driveways and sidewalks in the winter as a way to earn extra money. together they shoveled 450 square feet of sidewalk in 30 minutes. then melinda shoveled for 20 minutes while paula shoveled for 25 minutes to complete 345 square feet of driveway.\n30x + 30y = 450\n20x + 25y = 345\nhow much more can paula shovel in 1 minute than melinda?\n3 square feet per minute\n6 square feet per minute\n9 square feet per minute\n15 square feet per minute

Answer

Explanation:

Step1: Simplify the first - equation

Divide the equation $30x + 30y=450$ by 30. We get $x + y = 15$, which can be rewritten as $x=15 - y$. $$x + y = 15\Rightarrow x=15 - y$$

Step2: Substitute $x$ into the second - equation

Substitute $x = 15 - y$ into $20x+25y = 345$. [ \begin{align*} 20(15 - y)+25y&=345\ 300-20y + 25y&=345\ 300 + 5y&=345\ 5y&=345 - 300\ 5y&=45\ y&=9 \end{align*} ]

Step3: Find the value of $x$

Substitute $y = 9$ into $x=15 - y$. Then $x=15 - 9=6$.

Step4: Calculate the difference

We want to find how much more Paula ($y$) can shovel in 1 minute than Melinda ($x$). The difference is $y - x$. Substitute $x = 6$ and $y = 9$ into $y - x$, we get $9-6 = 3$.

Answer:

3 square feet per minute