Use AirPort as Time Machine whilst using internet I have an AirPort Time Capsule (model 802.11ac 2TB). I connect to the internet via my work's WiFi. I have managed to set up the AirPort as my Time Machine backup, and can connect to the device by switching my WiFi to the new WiFi network that the device creates. Although this allows me to perform backups, I cannot use the internet whilst I am connected to this WiFi device. Similarly, if I connect to my work's WiFi network, my MacBook cannot see the AirPort device and therefore cannot perform Time Machine backups.

How do I enable both use of the internet and background backups at the same time? Surely this must be possible.

Note that I have a spare ethernet socket nearby, which I could plug into the AirPort device if this helps. Or, if the AirPort device is capable of doing so, I could register the device on the network and connect it to the work WiFi as well.
You could connect your AirPort Time Capsule via Ethernet and turn off the box’s Wifi altogether. This way, it will become part of your existing (wireless?) network and you can back up and access the Internet at the same time.

Any Airport device can be set up in “bridge mode” and they will join a network like any other computer as opposed to making their own network and requiring correct routing setup.