Is there a word to describe the action that involves both running and walking?
I reached the destination by walk and sometimes running during the Journey.
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The name for that is "interval training."
Interval training can refer to the organization of any cardiovascular workout (e.g., cycling, running, rowing), but is particularly employed by runners, alternating between running and walking or slow jogging.
Interval training is a type of training that involves a series of high intensity workouts interspersed with rest or relief periods. The high-intensity periods are typically at or close to anaerobic exercise, while the recovery periods involve activity of lower intensity. Varying the intensity of effort exercises the heart muscle, providing a cardiovascular workout, improving aerobic capacity and permitting the person to exercise for longer and/or at more intense levels.
Many would understand you if you say:
"I interval train one hour every morning."
"Interval training" is pretty commonly understood because of the interval training mode found on nearly all treadmills that alternates the user between running and walking. However, if someone doesn't understand it, they can then ask you what that entails, or if you think they might not understand it, you could teach them what it means by being more elaborative and saying something like:
"I interval train one hour every morning, which involves alternating between running to build heart strength, muscle tone, and stamina and walking to burn fat and lower my BMI."
'On foot' includes both walking and running. See Merriam-Webster: 'by walking or running'.