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.How much more can Paul shovel in 1 minute than Melinda?

Answer 1

30x+30y=450

20x+25y=345

answer: 3 square ft per minute

Answer 2

Paul can shovel 3 sq feet per minute more than Melinda.

Explanation:

Let Melinda shovels per minute, 'x' sq feet area.

Let Paul shovels per minute, 'y' sq feet area.

Given - Melinda and Paul together shoveled 450 square feet of sidewalk in 30 minutes. Equation forms:

`30x+30y=450`

Factoring out 30 common, we get;

`x+y=15` .......(1)

Also given- Melinda shoveled for 20 minutes while Paul shoveled for 25 minutes to complete 345 square feet of driveway.

`20x+25y=345`

Factoring out 5 common, we get;

`4x+5y=69` ......(2)

Now, multiplying (1) by 4 and subtracting from (2) we get

y = 9

And
`x+9=15`

`x =15-9`

x = 6

So, we get that Melinda shovels 6 sq feet per minute and Paul shovels 9 square feet per minute.

This gives that, Paul can shovel
`9-6=3` sq feet per minute more than Melinda.