elise takes 12 minutes to rake up and bag a pile of leaves her sister katherine takes twice as long, how many minutes would it take both of them working together to complete 10 bags of leaves?

80 minutes

Step-by-step explanation:

Rate and Time are inverses of each other

First,

Elise Time = 12

and

Katherine Time = 2 * 12 = 24

Their rates would be (inverses):

Elise Rate = 1/12

Katherine Rate = 1/24

Together their rate is 1/12 + 1/24 = 3/24

Now, the inverse of this rate would be the time it takes to complete 1 bag together, that is:

(3/24) ^ - 1 = 24/3 = 8 minutes

So, 10 bags would take them:

8 * 10 = 80 minutes