Question

Melinda and Paul 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 Paul shoveled for 25 minutes to complete 345 square feet of driveway.

30x + 30y = 450
20x + 25y = 345
How much more can Paul shovel in 1 minute than Melinda?

Answer 1

Let x sq. ft be the area Melinda shovels per minute and y sq. ft be the area Paul shovels per minute.

1. Together they shoveled 450 square feet of sidewalk in 30 minutes, then

30x+30y=450.

2. Melinda shoveled for 20 minutes while Paul shoveled for 25 minutes to complete 345 square feet of driveway. Then

20x+25y=345.

3. Solve the system of equations:

$\left\{\begin{array}{l}30x+30y=450\\20x+25y=345.\end{array}\right.$

Divide the first equation by 30 and the second one by 5:

$\left\{\begin{array}{l}x+y=15\\4x+5y=69.\end{array}\right.$

From the first equation $x=15-y$ and

$4(15-y)+5y=69,\\ \\60-4y+5y=69,\\ \\y=9\ ft^2.$

Then $x=15-9=6\ ft^2.$

Paul can shovel $9-6=3\ ft^2$ more than Melinda can.

Answer 2

Answer:

Paul can shovel 3 square feet more than Melinda in one minute.

Step-by-step explanation:

Let Melinda shovels driveways in x square feet in one minute and Paul shovels y square feet in one minute.

From first statement of the question.

Together they shoveled 450 square feet in 30 minutes.

Then equation will be 30x + 30y = 450

We solve it further dividing by 30 on each side of the equation.

x + y = 15 -------(1)

Second statement says Melinda shoveled for 20 minutes and Paul shoveled for 25 minutes to complete 345 sq. feet.

The equation will be 20x + 25y = 345

Further we divide the equation by 5

4x + 5y = 69--------(2)

Now we multiply equation 1 by 4 and subtract it from equation 2.

(4x + 5y) - (4x + 4y) = 69 - 60

y = 9

by putting the value of y in equation number 1.

x + 9 = 15

x = 15 - 9 = 6

Now we have to find the difference between per minute shovel done by Paul and Melinda.

y - x = 9 - 6 = 3

Therefore Paul can shovel 3 square feet more than Melinda.