David and Josh are both practicing for an upcoming swim tournament. Every week, David swims for 3x hours at an average speed of x laps per h

Question

David and Josh are both practicing for an upcoming swim tournament. Every week, David swims for 3x hours at an average speed of x laps per hour. Josh swims 5 more hours per week than David, but at an average speed that is 4 laps per hour less than David’s average speed.

Which of the following functions will give the total distance, in laps, that Josh swims each week?

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Answers ( No )

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    2021-09-09T19:40:41+00:00

    Answer: 3x^2 – 7x – 20

    Explanation:

    This questions has 4 answer choices to select the right one.

    These are the answer choices:

    A) f(x) = 3x^2 – 17x + 20
    B) f(x) = 3x^2 + 7x – 20
    C) f(x) = 3x^2 – 7x – 20
    D) f(x) = 3x^2 + 17x + 20

    Solution:

    Translate the given word statements into algebraic expressions:

    1) Every
    week, David swims for 3x hours at an average speed of x laps per hour =>

    time = 3x
    speed = x

    2) Josh swims 5 more hours per week than David =>

    time = 5 + 3x

    speed
    that is 4 laps per hour less than David’s average speed =>

    speed = x – 4

    3) distance, in laps, that Josh swims each week, equal time * speed

    => distance = (3x + 5) (x – 4)

    4) Expand the parenthesis:

    a) distributive property: (3x)(x) + (3x)(-4) + 5(x) + 5(-4) = 3x^2 – 12x + 5x – 20 =

    = 3x^2 – 7x – 20

    Answer: 3x^2 – 7x – 20 (option C)

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