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?

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)

3x = 5 (x-4)

I am not sure about the equal sign though.