Let x represent the walking rate
Let y represent the jogging rate
Recall,
time = distance/speed
If you walk 6 miles, then the time spent walking is 6/x
If you jog at three times your walking speed, it means that
y = 3x
Since the distance covered by jogging is 6 miles, then the time spent jogging is
6/3x
= 2/x
If the total time spent walking and jogging is 4 hours, it means that
6/x + 2/x = 4
If we cross multiply by x, it becomes
6 + 2 = 4x
8 = 4x
4x = 8
x = 8/4
x = 2
y = 3x = 3 * 2
y = 6
Thus,
Walking rate is 2 miles per hour
Jogging rate = 6 miles per hour