Create a piecewise function of the following scenario where

Create a piecewise function of the following scenario where D(t) is the total distance walked (in miles), You begin a walk from your home at a fast pace of 3 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.

D(t)=_________ if 40 < t < or equal to 65

Solution

distance D(t) covered in first 25 minutes

distance = speed* time

speed for first 25 minutes = 3 miles / hour = .05 miles / minute

D(t) = .05 * t = .05 t for first 25 minutes

then he rests for 15 minutes

so, distance covered would be 0

and walks at 1mile/ hour for another 25 minutes that is 40 + 25 = 65

D(t) = .0166* t = .0166 t

piecewise function is

D(t) = .05* t   if 0 < t <= 25

D(t) = 0   if 25 < t <= 40

D(t) = .0166 t   if 40 < t <= 65