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 veloc

Question

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?

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Adeline 3 weeks 2021-12-29T01:47:51+00:00 1 Answer 0 views 0

Answers ( )

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    2021-12-29T01:49:01+00:00

    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, d and d.

    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,

    d + 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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