Last April the New York Times came out with an article about 9 minutes being enough for strength training. There is a science to back this length of time for strength training that proves to improve health effectively. The workout consists of 3 sets of 3 minutes each that does not require equipment. However, it must be done at a high intensity level and will strengthen lungs, muscles, and heart.
Based on this article, one hour and 45 minutes is too long if you are not a professional athlete because this is the average work-out session for strength training of a paid athlete during off-season. During the season, professional athletes will only spend a maximum of one hour on strength training. The reason for this is they want to avoid burn-out and fatigue.
Realistically, the length of your strength training should be based on your personal demographics and goals. If you are young and eager, you can train longer but if you are in your 40s, you need to slow down and listen to your body. Other factors include the type of strength training you plan to do. For instance, if you want to build muscle, the actual drills should only last for 20 seconds with around 40 seconds rest time. For endurance, you need to work-out at 30 seconds cycles with 30 seconds rest time adjusting if the intensity increases or decreases. The reason for the rest time is to give your body time to recover from the strain and to build energy for the next cycle.
Based on other scientific research, when doing strength training, always prioritize your most important training goals at the start and allow for longer rest time the higher your intensity level is. Also, keep in mind that strength training is either compound training or isolation training. This means, you chose to exercise a set of muscles or body areas or focus on single goals.
If your muscles are sore after workout, use a foam roller.