Well, I have a brief explanation of speedwork (below), which is some of what you're asking. A "split" usually refers to the time it took to run part of a longer run. So you can talk about your mile splits on a 10-mile run, that is, your time at each mile marker. When/if you do speedwork depends on your goals as a runner. Generally these workouts are designed to get faster. You should do no more than two speed sessions per week. Hope this answers most of your questions.

Len

• Intervals: This is the "4x400", etc, said four by four hundred. That means doing four repeats of four hundred meters (1/4 mile) at a fast pace. Warmup for a mile or so. Do the first fast "repeat" of 400 meters, followed by a slow recovery "interval" (where the name comes from) of about the same time as the repeat. So if the repeat takes 2:15 (minutes:seconds), so should the recovery. Do this three more times for a total of four (thus 4x400). All of the repeats are preferably done in the same time or possibly getting slightly faster (a second or two) as you go along. Intervals are best done on a track, or on a precisely measured course, the flatter the better.
• Hill repeats are something like intervals, except you run up a hill (150 to 300 meters) for the hard part, then down easy for recovery, repeat.
• Tempo Runs: Warm up for a mile or so. Do a specified distance (or time) at "tempo" pace (I'll get to that). Cool down for a mile or so. The tempo distance/time is usually a minimum of 2 miles or 20 minutes, and it goes up from there. To some extent it depends on what you're training for: shorter for short races, longer for long races. Tempo pace (also called "lactate threshold" pace) is a fast (race level fast) pace you can hold for about an hour. So a 10-mile race pace is frequently used (1/2 marathon pace for faster runners). The pace can be figured from other length races (5K or 10K for instance). The McMillan Running Calculator will figure paces for these workouts based on a recent race time: http://www.mcmillanrunning.com/mcmillanrunningcalculator.htm
• Fartlek: Also know as speedplay. This is "pickups" of varying distance during an otherwise regular training run. Warmup for the first mile. Pick up the pace to some arbitrary point down the road, a telephone pole, side street, sign, etc. Slow to your normal pace for a while, then do another pickup. The number and distance are up to you.
• Strides - Strides are short, quick accelerations usually done at the end of a regular training run. They are fast but not sprints, 50 to 100 strides/steps (counting both feet), typically repeated 4 to 10 times, with an equal slow recovery after each. Accelerate for 10-15 steps at the beginning, run the middle part at a quick pace, decelerate for 10 or 15 steps.

Speedwork, hill repeats and long runs are generally considered "hard" workouts. Avoid doing hard workouts on consecutive days. Always take a rest/recovery/cross-training day in between.

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Forget about reason, forget about rhyme. Beg, steal or borrow, you got another hill to climb.

G. Lightfoot