Question

Bill bikes 4 km to school. After 5 min he is 3.2 km from the school. The graph of the function that models Bill's distance to school is shown in red. Because of hills and traffic conditions along the way, Bill's speed varies. Nevertheless, a linear function, whose graph is shown in blue, can also be used to model his distance as a function of his time spent bicycling. a) Give an equation of the linear function. b) Use the equation to find approximately how long it takes Bill to bicycle to school.

Answer 1

The equation of the linear function modeling Bill's distance to school over time is d(t) = 4 - 0.16t. To find the time it takes for Bill to reach school, we solve for t when d(t) = 0, which gives us 25 minutes.

Step-by-step explanation:

To answer the student's question, we first establish the linear function that models Bill's distance to school as a function of time.

Given that Bill is 4 km away from school at the start and 3.2 km away after 5 minutes, we can determine two points on the linear graph: (0, 4) and (5, 3.2). The slope (δy/δx) of the line can be calculated as (3.2 - 4) / (5 - 0) = -0.16 km/min, representing Bill's average speed.

The y-intercept is the initial distance from school, which is 4 km. Therefore, the equation of the line is d(t) = 4 - 0.16t, where d(t) is the distance from school and t is the time in minutes.

To determine how long it takes Bill to reach school, we set the distance d(t) to 0 and solve for t. This gives us 0 = 4 - 0.16t, which simplifies to t = 4 / 0.16, resulting in t = 25 minutes. Hence, Bill takes approximately 25 minutes to bicycle to school.