Jeff Can Walk Comfortably At 3.75 Miles Per Hour. Find A Linear Function \[$d(t)\$\] That Represents The Total Distance Jeff Can Walk In \[$t\$\] Hours, Assuming He Doesn't Take Any Breaks.$\[ D(t) = 3.75t \\]

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Understanding Linear Functions: A Real-World Example

In mathematics, a linear function is a polynomial function of degree one, which means it has the form of a straight line. It is defined as a function that can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. In this article, we will explore a real-world example of a linear function, which represents the total distance Jeff can walk in a given number of hours.

Jeff can walk comfortably at a speed of 3.75 miles per hour. We want to find a linear function that represents the total distance Jeff can walk in t hours, assuming he doesn't take any breaks. In other words, we want to find a function d(t) that gives us the total distance Jeff can walk in t hours.

To find the linear function d(t), we need to use the formula for distance, which is:

d = rt

where d is the distance, r is the rate (or speed), and t is the time.

In this case, the rate (or speed) is 3.75 miles per hour, and the time is t hours. Therefore, we can plug these values into the formula to get:

d(t) = 3.75t

This is the linear function that represents the total distance Jeff can walk in t hours.

Now that we have found the linear function d(t) = 3.75t, let's interpret what it means. The function tells us that the total distance Jeff can walk in t hours is equal to 3.75 times the number of hours he walks. For example, if Jeff walks for 2 hours, the total distance he can walk is:

d(2) = 3.75(2) = 7.5 miles

This means that Jeff can walk a total distance of 7.5 miles in 2 hours.

To visualize the function, we can graph it on a coordinate plane. The graph of the function d(t) = 3.75t is a straight line that passes through the origin (0,0). The slope of the line is 3.75, which represents the rate at which Jeff walks.

The linear function d(t) = 3.75t has several important properties that we should note:

  • Domain: The domain of the function is all real numbers, which means that Jeff can walk for any number of hours.
  • Range: The range of the function is all non-negative real numbers, which means that the total distance Jeff can walk is always non-negative.
  • Slope: The slope of the function is 3.75, which represents the rate at which Jeff walks.
  • Y-intercept: The y-intercept of the function is 0, which means that Jeff can walk a total distance of 0 miles if he doesn't walk at all.

The linear function d(t) = 3.75t has several real-world applications. For example:

  • Distance calculation: The function can be used to calculate the total distance Jeff can walk in a given number of hours.
  • Time calculation: The function can be used to calculate the time it takes for Jeff to walk a given distance.
  • Speed calculation: The function can be used to calculate the speed at which Jeff walks.

In this article, we explored a real-world example of a linear function, which represents the total distance Jeff can walk in a given number of hours. We found the linear function d(t) = 3.75t and interpreted its meaning. We also graphed the function and noted its properties. Finally, we discussed several real-world applications of the function.
Jeff's Walking Distance: A Linear Function Q&A

In our previous article, we explored a real-world example of a linear function, which represents the total distance Jeff can walk in a given number of hours. We found the linear function d(t) = 3.75t and interpreted its meaning. In this article, we will answer some frequently asked questions about Jeff's walking distance.

Q: What is the domain of the function d(t) = 3.75t?

A: The domain of the function d(t) = 3.75t is all real numbers, which means that Jeff can walk for any number of hours.

Q: What is the range of the function d(t) = 3.75t?

A: The range of the function d(t) = 3.75t is all non-negative real numbers, which means that the total distance Jeff can walk is always non-negative.

Q: What is the slope of the function d(t) = 3.75t?

A: The slope of the function d(t) = 3.75t is 3.75, which represents the rate at which Jeff walks.

Q: What is the y-intercept of the function d(t) = 3.75t?

A: The y-intercept of the function d(t) = 3.75t is 0, which means that Jeff can walk a total distance of 0 miles if he doesn't walk at all.

Q: How can I use the function d(t) = 3.75t to calculate the total distance Jeff can walk in a given number of hours?

A: To calculate the total distance Jeff can walk in a given number of hours, simply plug the number of hours into the function. For example, if Jeff walks for 2 hours, the total distance he can walk is:

d(2) = 3.75(2) = 7.5 miles

Q: How can I use the function d(t) = 3.75t to calculate the time it takes for Jeff to walk a given distance?

A: To calculate the time it takes for Jeff to walk a given distance, simply divide the distance by the rate (or speed). For example, if Jeff wants to walk a distance of 15 miles, the time it will take him is:

t = d/r = 15/3.75 = 4 hours

Q: How can I use the function d(t) = 3.75t to calculate the speed at which Jeff walks?

A: To calculate the speed at which Jeff walks, simply divide the distance by the time. For example, if Jeff walks a distance of 10 miles in 2 hours, the speed at which he walks is:

r = d/t = 10/2 = 5 miles per hour

Q: What if Jeff takes breaks while walking? How can I account for this in the function d(t) = 3.75t?

A: If Jeff takes breaks while walking, the function d(t) = 3.75t will not accurately represent the total distance he can walk. In this case, you will need to modify the function to account for the breaks. One way to do this is to add a term to the function that represents the distance Jeff walks during each break.

In this article, we answered some frequently asked questions about Jeff's walking distance. We hope this Q&A has been helpful in understanding the linear function d(t) = 3.75t and its applications.