Final answer:
To find out how long it will take Avery and Madeline to sweep the deck together, we can find their individual rates and combine them. Their combined rate will give us the time it will take to complete the task together.
Step-by-step explanation:
To find out how long it will take Avery and Madeline to sweep the deck together, we can use the concept of rates. Avery can sweep the deck in 5 minutes, which means she can sweep 1/5 of the deck in 1 minute. Madeline can sweep the deck in 7 minutes, which means she can sweep 1/7 of the deck in 1 minute.
To find out how long it will take them to sweep the deck together, we can add their rates. 1/5 + 1/7 = 7/35 + 5/35 = 12/35. So together, they can sweep 12/35 of the deck in 1 minute.
To find the time it will take them to sweep the entire deck, we can divide 1 by their combined rate: 1 / (12/35) = 35/12. Simplifying, we find that it will take them approximately 2.92 minutes to sweep the deck together.