Luke rides his bike to his aunt's house. He travels 10 mi/h. Because it starts to rain, Luke's aunt drives him home in a car traveling at 25 mi/h. It takes Luke 1.5 h longer to get to his aunt's house than to return home. How many hours did it take Luke to ride to his aunt's house?

2.5 hours

Step-by-step explanation:

Let t = time in hours for reach friend's house

(t-1.5) = time for friend to drive her home

:

Both trips are the same distance, Write a distance equation from this fact:

Distance = speed * time

Drive distance = Bike distance

Equation-

step1)   25 (t-1.5) = 10t          (here u multiply 25 by t and 25 by 1.5)

step2)  25t - 37.5 = 10t        (move 37.5)          

step3)  25t - 10t = +37.5      (subtract 25t from 10t)

step4)  15t = 37.5                 (divide 37.5 by 15)

step5)  t = 2.5                     (time it took Luke to reach his aunt's house)

step-by-step explanation:

im not sure what the answer is

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)