## 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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1. Answer: 3x^2 – 7x – 20

Explanation:

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

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)