Create a piecewise function of the following scenario where Upper D left-parenthesis t right-parenthesis 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 3 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."

How far have you walked at the end of 23, 39, and 55 minutes?

Round your answers to two decimal places

Upper D left-parenthesis t right-parenthesis ??

really? This is math, not English!

D(t) =
3(t/60) if 0<t<=30
1/2 if 30<t<=40
1/2 + 1((t-40)/60) if t>30

To create a piecewise function for the given scenario, we need to break down the time intervals and the corresponding walking speeds. Let's break it down step by step:

1. "You begin a walk from your home at a fast pace of 3 miles per hour for 30 minutes."
This means that for the first 30 minutes, you are walking at a speed of 3 miles per hour. Therefore, within this time interval, you will cover a distance of 3 miles per hour * (30 minutes / 60 minutes per hour) = 1.5 miles.

2. "You rest for 10 minutes"
During this interval, you are not walking, so there is no distance covered.

3. "You continue walking at a leisurely pace of 1 mile per hour for 25 minutes."
For the next 25 minutes, you are walking at a speed of 1 mile per hour. Hence, within this time interval, you will cover a distance of 1 mile per hour * (25 minutes / 60 minutes per hour) = 0.4167 miles.

Now, let's create the piecewise function for the total distance walked (Upper D left-parenthesis t right-parenthesis) as a function of time (t).

For t ≤ 30 minutes: Upper D left-parenthesis t right-parenthesis = 3t/60

For 30 minutes < t ≤ 40 minutes: Upper D left-parenthesis t right-parenthesis = 1.5 miles

For 40 minutes < t ≤ 65 minutes: Upper D left-parenthesis t right-parenthesis = 1.5 + (t - 40)(1/60)

To find the distances walked at the end of 23, 39, and 55 minutes, we substitute these values into the piecewise function:

At t = 23 minutes:
For 0 < t ≤ 30 minutes: Upper D left-parenthesis t right-parenthesis = 3t/60 = 3(23)/60 = 1.15 miles (rounded to two decimal places).

At t = 39 minutes:
For 30 minutes < t ≤ 40 minutes: Upper D left-parenthesis t right-parenthesis = 1.5 miles = 1.5 miles (no rounding needed).

At t = 55 minutes:
For 40 minutes < t ≤ 65 minutes: Upper D left-parenthesis t right-parenthesis = 1.5 + (t - 40)(1/60) = 1.5 + (55 - 40)(1/60) = 1.5833 miles (rounded to two decimal places).

Therefore, at the end of 23, 39, and 55 minutes, you have walked distances of approximately 1.15 miles, 1.5 miles, and 1.58 miles, respectively (rounded to two decimal places).