It is possible that they are overusing the router and exceeding the switching bandwidth that the router is able to do by transferring a large amount of files between multiple computers at the same time.
The more likely scenario is that you are all fighting over the limited bandwidth that the ISP is providing.
Going back to the new car to try to fix your commute example ...
1. You could ask everyone to nicely don't drive as much / download less.
2. You could pour water into everyone's virtual car's gas tank so that it drives slower using a feature on the router called Quality of Service that is able to regulate the speed of computers and applications on an individual basis.
I would ask the I.T person that controls the router if he could do this to make the download speeds more fair.
For instance, if you have a 24 megabit connection and 24 people you could guarantee everyone 1 megabit instead of one guy hogging 20 megabits and everyone else splitting the left over 4 megabits, which appears to be happening now.
I use an Asus RT-AC66R modem and it is able to do QOS.
https://www.asus.com/support/FAQ/1010934/
If your phone has a large enough data plan you can tether it to your laptop and use it for internet.
I have this as a backup in case my Internet connection ever goes down.