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 25 minutes. You rest for 15 minutes, and then you continue walking at a leisurely pace of 1 mile per hour for 25 minutes."
I have 1/10t, 0<t<25
2.5, 25<t<40
and need to find the last equation for the domain of 40<t<65
well, you correctly determined that 6 mi/hr is 1/10 mi/min, so
1 mi/hr is the same as 1/60 mi/min, right?
y = 2.5 + 1/60 t for 40<t<65.
Actually, some of those inequalities should be <= just to make D(t) continuous.
To create the last equation for the domain of 40 < t < 65, let's analyze the scenario described:
Initially, you walk for 25 minutes at a pace of 6 miles per hour. In this time period, you cover a distance of (6 miles/hour) * (25/60) hours = 2.5 miles. Therefore, the function D(t) for this duration will be constant and equal to 2.5.
After that, you rest for 15 minutes, and no distance is covered during this time. Hence, the function D(t) remains constant at 2.5 for 25 < t < 40, including the 15-minute rest period.
Now, we need to figure out the function for the domain of 40 < t < 65, where you continue walking at a leisurely pace of 1 mile per hour for 25 minutes.
Since you walk at a pace of 1 mile per hour, in 25 minutes, you'll cover a distance of (1 mile/hour) * (25/60) hours = 0.4167 miles. As this distance is covered within the interval of 40 < t < 65, the function D(t) will be constant and equal to 2.5 + 0.4167 = 2.9167.
Therefore, the piecewise function representing this scenario is:
D(t) = 1/10t, 0 < t < 25
2.5, 25 < t < 40
2.9167, 40 < t < 65