This tube or hose fits perfectly on the outside of the cooler (this doesn't sound right in my ear languagewise, I'll better explain further
).
The hose with the smaller diameter is to push inside the connection on the cooler. With the rubber on the washing machine hose, you do it the other way, you push it over the connection...
Tbh, it wasn't my idea, but it works just great. Look here:
https://youtu.be/-DxEmb-2s2A?t=301 (starts at 5:01, were you can see the hose). At 5:14, you see what I'm trying to explain in my bad english (sorry).
EDIT: the rubber in the washing machine hose is more like a universal adapter
