Avery can sweep the deck in 5 minutes and Madeline can do it in 7 minutes. How long will it take them to do it together?​

Avery in 5 minutes sweeps 1 deck, so in 1 minute she sweeps 1/5 of the deck

Madeline in 7 minutes sweeps 1 deck so in 1 minute she sweeps 1/7 of the deck.

1/5 + 1/7 = 7/35 + 5/35 = 12/35

Together they will sweep 1 deck in x minutes : 1/x

12/35 = 1/x =

X = 35/12 = 2.92 minutes. ( round the answer as needed)

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.