Lizette is training for a marathon. at 7: 00 she left her house and ran until 8: 15, then she walked until 11: 15. she covered a total distance of 19 miles. her running speed was 5 miles per hour faster than her walking speed. find her running and walking speeds.

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.