Will taking these steps help me to loose weight?

I just joined a gym and am trying to get healthier! (yay!) but anyways, will going for a 40 minute run on the treadmill at about 5-5.5 speed and doing 20 minutes on the elliptical (with the arm blaster on) help me slim down? Of course I'm going to start eating healthier too and drinking more water. Will this help me out? Im in pretty decent shape but Im kinda chubby around the tummy so I want to slim down a tad. thanks all!