Mathematics, 26.04.2020 09:58 poppy4195

Courtney camino desde su casa a la playa a una velocidad constante de 4 kilómetros por hora, y luego de la
playa al parque a una velocidad constante de 5 kilómetros por hora. La caminata completa tomó 2 horas y
la distancia total que Courtney recorrió fue 8 kilómetros.
Sea b el número de horas que le llevó a Courtney caminar de su casa a la playa y sea p el número de horas
que le llevó caminar de la playa al parque.
¿Cuál sistema de ecuaciones representa esta situación?

Answers: 3

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Answers

Answer from: shadoris26

Queremos encontrar un sistema de ecuaciones para la situación dada. Veremos que el sistema es:

D = (4km/h)*bC = (5km/h)*pD + C = 8kmp + b = 2h

Primero, es fundamental recordar la relación:

Distancia = velocidad*tiempo.

Sabemos que Courtney va de su casa a la playa a 4km/h, se la D distancia entre su casa y la playa y b el tiempo que tarda en llegar, entonces tenemos:

D = (4km/h)*b

Luego va de la playa al parque a 5km/h, sea C la distancia de la playa al parque y p el número de horas que tarda en llegar, entonces tenemos:

C = (5km/h)*p

Finalmente, sabemos que la distancia total que recorre es 8km y el tiempo total es 2 horas, entonces tenemos:

D + C = 8km

p + b = 2h

Así encontramos 4 ecuaciones para 4 variables, entonces el sistema de ecuaciones es:

D = (4km/h)*bC = (5km/h)*pD + C = 8kmp + b = 2h

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Answer from: britney9285

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.

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