Question

Steve and brian are both avid bicyclists. each week, steve rides for a total of 2x hours at an average speed of x miles per hour. brian rides 6 more hours a week than steve, but at an average speed that is 4 miles per hour less than steve's average speed. which of the following functions will give the total distance that brian rides each week, in miles?

1) m(x) = 2x² + 8x - 24
2) m(x) = 2x² + 24
3) m(x) = 2x²
4) m(x) = 2x² - 2x - 24

Answer 1

Brian's weekly biking distance is represented by the function m(x) = 2x^2 - 2x - 24, which accounts for his longer riding time and slower speed compared to Steve.

Step-by-step explanation:

The question asks for the function that will give the total distance that Brian rides each week, given that Steve rides for a total of 2x hours at an average speed of x miles per hour, and Brian rides 6 more hours a week than Steve at an average speed that is 4 miles per hour less than Steve's.

To find Brian’s total weekly distance, first calculate the number of hours he rides: 2x + 6 hours. Then, find his average speed, which is x - 4 miles per hour. Multiply these to find the total distance Brian rides each week: m(x) = (2x + 6)(x - 4).

Expanding the function, m(x) = 2x2 + 6x - 8x - 24, simplifies to m(x) = 2x2 - 2x - 24. Therefore, the correct answer is function 4: m(x) = 2x2 - 2x - 24.