Lizette ran for 1.25 hours and walked for 3 hours.
distance = speed × time
Her total distance is the sum of her distances at the different speeds. Let w represent her walking speed in mi/h. For distances in miles, speeds in miles per hour, and time in hours, the problem statement tells us ...
19 = (w+5)(1.25) + (w)(3)
19 = 4.25w + 6.25 . . . . collect terms
12.75 = 4.25w . . . . . . . subtract 6.25
3 = w . . . . . . . . . . . . . . . divide by 4.25
Lizette's walking speed is 3 mph.
Lizette's running speed is 8 mph.
