An aquarium tank can hold 7700 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 44 minutes. The second pipe can fill the tank in 77 minutes by itself. When both pipes are working together , how long does it take them to fill the tank ?

Pipe 1 works at a rate of (1 tank)/(44 min) = 1/44 tank/min.

Pipe 2 works at a rate of (1 tank)/(77 min) = 1/77 tank/min.

Together, both pipes work at a rate of (1/44 + 1/77) tank/min = 1/28 tank/min.

In this context, 1 tank = 7700 L. So when both pipes are working, water is flowing into the tank at a rate of

(1/28 tank/min) * (7700 L/tank) = 7700/28 L/min = 275 L/min

It then stands to reason that it would take 28 min for both pipes to fill the tank, since

(275 L/min) * (28 min) = 7700 L

answer:   (s+1)(s+4)

step-by-step explanation:

factor s2+5s+4

s2+5s+4

=(s+1)(s+4)

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)