Create a piecewise function of the following scenario where D(t) is the total distance walked (in miles) as a function of time t (in minutes): “You begin a walk from your home at a fast pace of 6 miles per hour for 30 minutes. You rest for 10 minutes, and then you continue walking at a leisurely pace of 1 mile per hour for 25 minutes."

I have 1/10t, 0</t</30
3, 30<t</40

BUT i cant find the last equation for the domain of
D(t)= __?__ if 40<t</65

In the first 30 minutes you have walked 3 miles. Then, after a total of 40 minutes, you start walking again. So,

D(t) = 3 + 1/60 (t-40) if 40 < t <= 65

@steve thank you

To find the equation for the last domain of the piecewise function, we need to determine the distance walked during that time period.

From the given scenario, we are walking at a leisurely pace of 1 mile per hour for 25 minutes.

Since the formula for distance is speed multiplied by time, and in this case the speed is 1 mile per hour, we can calculate the distance walked during this time period.

Distance = Speed * Time = 1 mile/hour * 25 minutes = 1/60 mile/minute * 25 minutes = 25/60 mile

Therefore, the equation for the last domain of the piecewise function is:

D(t) = 25/60, 40 < t ≤ 65

This means that during the time period 40 to 65 minutes, the total distance walked is 25/60 mile.

To create the piecewise function for the given scenario, we need to break it down into the different time periods and calculate the distances walked during each period.

First, we calculate the distance walked during the fast-paced period of 30 minutes at 6 miles per hour. Since distance is speed multiplied by time, we have:

Distance = 6 miles/hour * (30 minutes / 60 minutes/hour) = 6 * 0.5 = 3 miles

During the resting period of 10 minutes, no distance is covered, so we can assign a value of 0 for this duration.

Next, we calculate the distance walked during the leisurely-paced period of 25 minutes at 1 mile per hour:

Distance = 1 mile/hour * (25 minutes / 60 minutes/hour) = 1 * (25/60) = 25/60 = 5/12 miles

Now, we have the distances covered during the first two time periods:

D(t) = 3, 0 ≤ t ≤ 30
D(t) = 0, 30 < t ≤ 40

To find the distance covered during the final time period of 25 minutes while walking at an unknown pace, we need to recognize that the speed is not given. Therefore, we cannot accurately determine the distance for this period. As a result, we cannot write a specific equation for this part of the piecewise function.

Instead, we can write the equation as:

D(t) = __?__, 40 < t ≤ 65

Until the pace for the final period is known, we cannot calculate the distance.