The LAN will operate at the 10 Mbps.
This is because a hub is a kind of straight through connection. Unlike a switch, a HUB cannot differentiate one speed from another and must operate at 10BaseT – it is as though there is nothing there, no hub, and the (3) computers were (somehow) directly connected to eachother and had to operate at 10BaseT so the the slower NIC would be compatible.
Regardless, hubs allow transmission at half-duplex only. Suppose in this situation of mixing ethernet technologies that routers or switches had not been invented yet. However, you had a hub that supported 100BaseT. One of the computers connected to the hub handled routing for that hub. You still couldn’t mix the speeds. Hubs transmit at
half-duplex or in other words could be compared with having only a single channel and can only communicate in one direction at a time, either send or receive but not both at the same time. The computer you dedicated to handle routing couldn’t direct traffic on the network at all. Because you only have a single direction all traffic on the LAN could be described as being ‘blasted’ to every NIC on the network. So, your connection would have to be at 10BaseT for the sake of the slower machine. If it was 100-BaseT the slower NIC would crash as it tried to check packets (the traffic) for packets with it’s MAC in the header of the packet.
That’s why the hub will operate at the slower speed. If you had a switch on the other hand, it transmits at full-duplex or bi-directionally and its on-board processor can use the full-duplex capability to send/receive traffic to each technology individually.