Anton's family drove 216 mi to the lake averaging 48 mi/h . on the return trip home they averaged 54 mi/h . what was the total time that anton's family spent driving to and from the lake? 8.0 h 8.5 h 9.0 h 9.5 h

For this case we have that the distance that it is necessary to cross to arrive at the lake is of 216 miles.

If the family went there with an average of

To know the time it took me to travel 216 miles, we make a rule of three:

Let "x" be the time spent going to the lake:

48 miles -------------> 1 h

216 miles -----------> x

Thus, to reach the lake they had to travel 4.5 hours.

Now, back home they averaged

To know how much time they used back home, we make a rule of three (to return also travel 216 miles):

Let "y" be the time spent returning home:

54 miles -------------> 1 h

216 miles -----------> y

Thus, the total time is given by:

8.5 hours

Option B

b and c

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)