Write a function that models the following description: A man drove a total of 40 miles over a 2-hour period. (1 point)
f(_)=_
f(t) = 40-20t
To model a function based on the given description, we can use the concept of average speed. The average speed is defined as the total distance traveled divided by the total time taken.
Let's define the function f(t), where t represents the time in hours. We can write the function as:
f(t) = 40/2 = 20
This function calculates the distance traveled at any given time t, assuming a constant speed. Since the speed is constant, the distance traveled in any 2-hour interval will always be 40 miles.
To model the given description, we can define a function that calculates the man's distance traveled at any given time during the 2-hour period.
Let's assume that the man maintains a constant speed throughout the journey. So, the distance traveled will be directly proportional to the time elapsed.
If we denote the time t in hours and the distance d in miles, we can set up a linear equation to represent the relationship:
d = r * t
Where:
- d is the distance traveled in miles
- t is the time elapsed in hours
- r is the constant rate of speed in miles per hour
Since the man drove a total of 40 miles over a 2-hour period, we can substitute the given values and solve for r:
40 = r * 2
r = 40 / 2
r = 20 miles per hour
Now, we have the rate of speed, r, which is 20 miles per hour. We can use this information to define our function:
f(t) = 20t
This function represents the distance traveled, f(t), as a function of time, t, during the 2-hour period.