Using a speed workout is an excellent way to build strength, endurance and cardiovascular fitness. In addition, it can be a great change of pace to ease the pain of sore joints; especially as we age.
The first thought that comes to your mind with the term "speed workout" may be that you will be be buzzing around the gym working as fast as you can to cram in as many reps as possible until you are dizzy. Luckily, that is not the case. It also has nothing to do with making you a faster runner. Although, there are workouts for that, if you want.
In the strength training content that I have written about elsewhere in this site, the theory and the corresponding workouts, has been to lift reasonably heavy weights in a controlled manner, using good form until you reach the point of failure. Typical reps in a set are somewhere between 8 and 12, depending on the exercise and the specific workout. Over the years, all that heavy weight can wear on your joints. Sure, your muscles are thanking you. You joints? Not so much.
In what I am referring to as a speed workout, you will still use good form and control the weight. The amount of weight will be enough that you can't just throw it around, but not so heavy that the first rep is already difficult. You will move at a more brisk pace on each rep and do 20 to 25 reps per set. This will give your muscles a similar amount of weight to move. It is just spread out over more repetitions. This will stress our muscles, keep your heart rate up and keep the pressure of heavy weights off your joints. Nowadays, this is often referred to as volume training.
Simply stated: less weight and more reps vs. more weight and fewer reps. This is the theory behind a lot of dumb bell work, kettlebell workouts, and other similar programs. Plus, if you don't have a lot of space or weight, you can still accomplish your weight loss goals with this style of workout. Either way, be sure to use enough weight to reach muscular failure in the last rep or two.
Whether you are young or old, there are good reasons to use this type of workout.
Whatever the reason, use good form. Intensity is the key. Work to failure. No matter the method, building muscle burns fat. Period!