You will have no problems on 70 through KC on a Saturday. The only things that could remotely effect traffic is if there were a race at the speedway on the KS side or if the Chiefs were in town on the MO side. Hitting traffic for those would be very unlikely as you would have to be passing through right before the events.
I-70 on the KS side of KC has almost no traffic, ever. The MO side backs up frequently during the weekday rush hours, but the delays are rarely more than 15-20 minutes and you will hit far more traffic for a much longer duration if you try to go around the south side or something. Just in case you end up going through KC during the week.
You should stop and check out KC anyway. It's physically impossible for me to drive through a large city and not stop and mess around. Even if it’s just to drive around Downtown for ten minutes. But that’s me.
BTW, I-70 across KS is a nice drive, but they are always working on it. Not sure if there are any 2-lane stretches right now or not. Volumes are low though, so it’s usually not much of a delay.
I-70 across MO is much busier. 70 in MO is now nice and smooth, but there is some work going on just east of KC that could delay you some.
If you plan on staying on 70 through St Louis, take the 370 Bypass in St Charles County, that will take you around a lot potential traffic and it’s faster. It will dump you back on 270 in North St Louis County (70 comes out of StL on the north side in Illinois. That is unless you want to drive down and at least check out the Arch or something

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