|I'm assuming you're talking about how long it takes to connect when you first boot after the desktop screen has fully loaded. A minute or more after that is not unusual. |
All (enabled) network adapters are enabled while booting, but a wireless connection requires that an additional program needs to load after that.
If you want to see what the difference is, disable your wireless adapter in it's configuration, shut down the computer, connect a network cable between your computer and the router, boot your computer. Your internet connection will work as soon as the desktop screen has fully loaded. (It may take a bit of time for it to connect the first time - after that it will connect right away.)
Even when another identical laptop has the identical wireless adapter, how long it takes to connect wirelessly when you first boot also depends on other factors - which router model you're connecting to, what type of wireless it is (e.g. G or N), how strong the signal is, etc., etc.
If your nephew and co-worker were connecting to the same router as you connect to at a similar distance from the router, the time it takes them to connect would be very similar.
A friend of mine got a delay of at least a minute with a wireless G adapter built into her HP laptop after the desktop screen was loaded, even when the laptop was new, connecting to a D-Link wireless B combo router / ADSL modem that was provided by her ISP . The same laptop connected the same wireless G adapter a bit faster to a standalone D-Link wireless G router connected to a standalone ADSL modem, but the difference wasn't all that signifcant. The routers were in the same room.
I have noticed similar when I have set up wireless connections for other people, and for myself when I tried that with my computers.
If you're talking about it taking a minute to connect after that, that's a different subject.
The stronger the connection is between your wireless adapter and the router, the more likely it will connect faster.
If both the wireless adapter and the router use wireless N, the more likely it will connect faster.
If you're using a wireless settings program that did not come with Windows itself, you may get a faster connection if you DO NOT use that utility and use Window's built in Wireless Zero program instead.