On their way up the hill, Jack and Jill were stopped by their parents. It seems the two of them were trying to skip out on some chores. They were told to mow the lawn, clean the kitchen, and sweep the leaves off the deck. If Jack can complete all the chores in 3 hours by himself and Jill takes only 2.25 hours to get all of it done on her own, how many minutes will it take for the two of them to get the work done together

77.14 minutes.

Step-by-step explanation:

Jack's time = 3 hours

Jill's time = 2.25 hours = 2 1/4 = 9/4 hours

Combined time = x

Rates :

Jack = 1/3 ; jill = 1 / 2.25 = 1 / 9/4 = 4 /9

Combined rate = 1/x

Setting up the equation :

1/3 + 4/9 = 1/x

Lcm of 3 and 9 = 9

(3 + 4) / 9 = 1/x

7/9 = 1/x

Cross multiply :

7x = 9

x = 9/7 hours

x = (9/7)* 60

x = 77.14 minutes

Combined time = 77.14 minutes.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2