Question

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.
$30x + 30y = 450$
$20x + 25y = 345$
how much more can paula shovel in 1 minute than melinda?
○ 3 square feet per minute
○ 6 square feet per minute
○ 9 square feet per minute
○ 15 square feet per minute

Explanation:

Step1: Simplify first equation

Divide $30x + 30y = 450$ by 30:
$$x + y = 15$$
Rearrange to get $x = 15 - y$

Step2: Substitute into second equation

Substitute $x = 15 - y$ into $20x + 25y = 345$:
$$20(15 - y) + 25y = 345$$
Expand and simplify:
$$300 - 20y + 25y = 345$$
$$300 + 5y = 345$$

Step3: Solve for y

Subtract 300 from both sides, then divide by 5:
$$5y = 345 - 300 = 45$$
$$y = \frac{45}{5} = 9$$

Step4: Solve for x

Substitute $y=9$ into $x = 15 - y$:
$$x = 15 - 9 = 6$$

Step5: Find the difference

Calculate $y - x$:
$$9 - 6 = 3$$

Answer:

3 square feet per minute