Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked
from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the
total distance Courtney walked was 8 kilometers.
Let 6 be the number of hours it took Courtney to walk from her house to the beach, and p the number of hours
it took her to walk from the beach to the park.
Which system of equations represents this situation?

A system of linear equations is a set of equations that have more than one unknown or variable. In these equations the unknowns are related to each other.

To propose a system of equations, you must first identify the unknowns or variables of the problem. For this you must know what you want to find out about the problem. And then a variable or letter must be assigned: One of the unknowns of the problem is called "q" and the other is called "p" (for this case)

In this case then:

"q" is the amount of hours it took Courtney to walk from her home to the beach.

"p" is the amount of hours it took him to walk from the beach to the park.

You know that the entire walk took 2 hours. This means that the amount of hours it took Courtney to walk from her home to the beach plus the amount of hours it took him to walk from the beach to the park must be 2. Expressed in an equation you get: p + q=2 Equation (A)

Now, the total distance Courtney walked was 8 kilometers. But you have as data the value of the speed at which Courtney walks from her house to the beach, and the speed at which she walks from the beach to the park.

But you should keep in mind that speed is equal to the distance traveled divided by time, or what is the same, distances are equal to speed by time.

[tex]speed=\frac{distance}{time}[/tex]

or

distance=speed*time

So, as the data you have are the aforementioned speeds, and the amounts of hours it took Courtney to walk from her house to the beach, and from here to the park, and from the beach to her house, it is possible to determine the distances of as follows, remembering the way in which the variables were defined:

From her house to the beach:

distance 1= 4 kilometers per hour* q

From the beach to the park:

distance 2= 5 kilometers per hour* p

As mentioned the total distance that Courtney traveled was 8 kilometers, this is the distance from her house to the beach plus the beach to the park was kilometers. Expressed in an equation you get: 5p + 4q=8 Equation (B)

Finally, the system of equations that represents this situation is

[tex]\left \{ {{p+q=2} \atop {5p+4q=8}} \right.[/tex]