I will answer your question with another question, “what kind of exercise are you talking about?” Cardiovascular changes/benefits occur with 30 to 45 minutes of Physical Activity a day over a period of two to three weeks. Cardiovascular fitness requires longer bouts of activity (at an intensity of at least 65% of your Predicted Maximum Heart Rate) to show adaptations. Cardiovascular fitness takes the most time and effort to improve and takes a very short time to lose. The nice thing is that Cardiovascular Fitness does not require a high exertion rate to show adaptation, but requires longer bouts of activity. So, you can walk at a moderate pace for 20 to 45 minutes to strengthen your cardiovascular system.
When it comes to strength training and resistance training, you do not have to train that long (but the intensity needs to be higher, that is the trade off). In order to show an improvement in muscular strength you need to perform resistance training exercises at an intensity that you perceive as somewhat hard on the Rate of Perceived Exertion Scale. The resistance training activity should be done to failure at a minimum of 8 reps and a maximum of 20 reps. If you can only do 8 repetitions, then this is a maximal exercise and it is not safe to do your first set at a maximal level. It is recommended that you perform one set of 12 to 15 repetitions for all the major muscle groups of the body to failure, with a frequency of 2 to 3 times per week. If you perform just the major muscle groups with one set of each exercise, you should be able to complete all the exercises in 10 to 15 minutes at a time.
It is recommended that you do one set of 12 to 15 repetitions to failure because it shows the greatest muscular strength adaptations. The increase in benefits to muscular strength by adding a second set is negligible and not recommended. If you choose a weight that begins to get hard on the 9th rep and increases intensity to the last rep, you will get the muscle adaptation that you are looking for without the higher risk of muscle injury with a maximal set (performing a maximal set requires maximal exertion during the first few repetitions and requires at least one warm up set to prevent injury to the muscle being worked).
Now that you have the information, you can decide on the amount of time you want to exercise and if you want to break it up. You can do your cardiovascular training during the day and then do your resistance training for 10 to 15 minutes a day at a set time (it is best to set a specific time to exercise and stick to it. This allows your body to get used to training at that time and helps you form a habit). Or, you can decide to go to the gym and do cardio for 20 – 45 minutes and then resistance training for 15 minutes every other day. This decision is based on preference.