Melissa walks 3 miles to the house of a friend and returns home on a bike. she averages 4 miles per hour faster when cycling than when walking, and the total time for both trips is two hours. find her walking speed.

s₁ = 2 m/s

Step-by-step explanation:

given,

distance between Melissa and friend = 3 mile

walking speed = s₁

bike speed = s₂

total time of the trip = 2 hour

given,

s₂ = s₁ + 4

2(s₁ +4)s₁ = 3 (s₁ + s₁ + 4)

2 s₁² + 8 s₁ = 6 s₁ + 12

s₁² + s₁ - 6 = 0

s₁² + 3 s₁ - 2 s₁ - 6 = 0

(s₁ + 3) (s₁ -2) = 0

s₁ = -3 , 2

s₁ = 2 m/s

walking speed of the Melissa is s₁ = 2 m/s

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is