Question

Courtney camino desde su casa a la playa a una velocidad constante de 4 kilómetros por hora, y luego de la

Answer 1

Answer:

The system of equations represents this situation is:

4b + 5p = 8 and b + p = 2.

Step-by-step explanation:

The question is:

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

Solution:

The formula to speed is:

$s=\frac{d}{t}$

Then the formula of distance traveled is:

$d=st$

Let the two distances traveled by Courtney be, d₁ and d₂.

It is provided that:

Speed at Courtney walked from her house to the beach was, s₁ = 4 km/h.

Speed at Courtney walked from the beach to the park was, s₂ = 5 km/h.

The total distance traveled is,

d₁ + d₂ = 8...(i)

It is assumed that,

b =  number of hours it took Courtney to walk from her house to the beach

p = number of hours  it took him to walk from the beach to the park

Then the equation (i) can be written as:

bs₁ + ps₂ = 8

⇒ 4b + 5p = 8

Also the total time it took to travel 8 kilometres is 2 hours.

Then,

$\frac{d_{1}}{s_{1}}+\frac{d_{2}}{s_{2}}=2\\\frac{bs_{1}}{s_{1}}+\frac{ps_{2}}{s_{2}}=2\\b+p=2$

Thus, the system of equations represents this situation is:

4b + 5p = 8 and b + p = 2.