how many minutes should I strength train for?

I recently bought a new gym membership and I got a free session with a personal trainer.  I worked out with the trainer last Monday, and now I'm so inpired to be doing resistance training regularly.  I could use some advice on how often, and for how long I should be doing these kinds of workouts. 

Is 3 times a week enough? 

Is 30 minutes (followed by cardio) adequate?  Would 60 be adequate, or is 60 min too much? 

I'd really appreciate any feedback.  Thanks!

there really can't be a time limit, 3 times a week is fine, as long as you are getting enough work.

Okay, but what about a time mimimum?  I have to budget my gym time around work, etc.  Can I reasonably expect to make progress if I'm only spending 30 minutes strength training?  Or do I need to look for some more time? 

The key is working the muscles, if you can work them hard in 15 minutes, then 15 minutes is enough. a total body workout 3 times a week should get you results, and 30 minutes should be fine as long as you are working hard.

I work out using weights 3x week for 30-40 minutes with a day of rest in between and so far I have not lost weight, but my pants and suit jackets are fitting a but looser. In my opinion 30 minutes of weights at a level that makes you feel like you worked hard is good.