To get a Bachelor of Science in engineering at most accredited schools, it takes a minimum of 4 years. From my experience, most people graduate in 4 to 5 depending on their internship and study abroad opportunities as well as how much work from high school transferred into credits - in other words take your AP classes as you can test out of a lot of material. I tested out of 18 credits (one whole semester). This gave me opportunities to do many other things and still graduate in 4 years, unlike many of my classmates.
And tell you cousin, engineering is awesome. Many say the schooling portion is tough, but definitely rewarding.