It takes Tim 4 hours to clean a house and it takes 3 hours for Amanda to do the same job. How long will it take for both of them to clean the house together?

1  5/7 hours

≈ 1 h 43 m

Tim 4 hours => 1 hours = 1/4 house

Amanda 3 hours => 1 hours = 1/3 house

Both 1 hour = ³⁾1/4 + ⁴⁾1/3 = (3+4)/12 = 7/12 house

How long will it take for both of them to clean the house together ?

12/12 (full house) : 7/12 =

= 12/12 ₓ 12/7

= 12/7 hours

= 1  5/7 hours

≈ 1 h 43 m

7.3

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)