Will coaxial cable installed in the 1970s be fast enough for internet speeds 400 Mb/s+?
Other than the pesky but unknown question of &quot;exactly which type is it&quot; coaxial cable has not really changed much in 50 years. If it's not defective, it will probably work. Otherwise, it's 50 feet, replace it, or let the provider replace it. Most providers will allow you to try a new service speed and decline if it does not work for you at the claimed speed.
Cable length (new or old) adds to loss of signal strength, and at some point that will affect what service you can get. More expensive, fatter, harder to bend cable can have less loss for the same distance at the same frequency. But it's rarely an issue in normal home-scale cable plants serviced by decent cable-company infrastructure (where they deal with providing enough signal strength to service most of their customers houses without extreme measures being required.) If your current modem permts you to view the signal strength it's getting, you might get some insight - otherwise the cable tech has a fancier meter that will let them know if it can work when they hook it up.
Why you &quot;upgraded&quot; from &quot;perfectly happy to do gigabit&quot; Cat5e to Cat6 for the prospect of possibly having 400 Mbit or even 1 gigabit is beyond me, though.