Eva wants to get to the bus stop as quickly as possible. The bus stop is across a grassy park, 2000 feet west and 600 feet north of her starting position. Eva can walk west along the edge of the park on the sidewalk at a speed of 6 ft/sec. She can also travel through the grass in the park, but only at a rate of 5 ft/sec (the park is a favorite place to walk dogs, so she must move with care). What path will get her to the bus stop the fastest

the path through the grass in the park is faster.

Step-by-step explanation:

The paths along which she can move forms a right angle triangle. The path along the west and north represents the opposite and adjacent sides of the triangle. The path through the grass in the park represents the hypotenuse. To determine the hypotenuse, h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

h² = 2000² + 600² = 4360000

h = √4360000

h = 2088.1 ft

If she walks along the side walk, her total distance is

2000 + 600 = 2600 feet

Eva can walk west along the edge of the park on the sidewalk at a speed of 6 ft/sec. It means that the time it will take her to walk along the sidewalk is

2600/6 = 433.3 seconds

She can also travel through the grass in the park, but only at a rate of 5 ft/sec. It means that the time it will take her to travel through the grass in the park is

2088.1/5 = 417.62 seconds

Therefore, the path through the grass in the park is faster.

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)