Here's a quick and effective workout for your back and biceps. Ideally, finish this workout in 20 minutes.
It's a very simple workout utilizing only chin-ups (palms facing you) and standard curls. Perform 1 pull-up and then 1 curl, 2 pulls-ups and then 2 curls, and so on until you reach 10 repetitions for each exercise. If you do all reps, you'll have completed 55 pull-up and 55 curls. A pretty simple, short, and effective workout.
I used a 25 lb weighted vest and 40 lb dumbbells. I completed 46 pull-ups and 45 curls. The last set was extremely difficult and it should be for you. If it's not, go with a heavier weight.