US 50 is one of the longest highways in the U.S. How long is it? Well, there's actually some debate on that (this page has more details about why that is).
Both the Maryland and California state departments of transportation have placed reciprocal mileage signs at the terminus points, each claiming the total distance is 3073 miles. This photo was taken in Ocean City MD, looking along the east beginning of US 50...
...and these next photos show signs that have been posted in Sacramento CA. The first one (and another one like it) were both stolen, so after that CalTrans changed their strategy by putting the mileage on a sign that is wider and more difficult to hijack:
In 2017 it was reported that Maryland was aware that figure of 3073 miles was incorrect. At the time they were thinking 3008 was a more accurate measurement, but they were going to verify before updating the mileage on the sign. As of May 2018, the old sign with 3073 remained, and the same was true on the Sacramento end as of August 2019.
3008 is pretty close, but according to the measurements I made in 2018, the actual distance is 3015 miles. If so, then the midpoint along US 50 would be at 1507.5 miles. That particular location along US 50 would be in Kansas, about five miles west of its junction with US 281 (or roughly between the towns of St. John and Macksville).
But of course all of those measurements are assuming US 50's current western terminus in Sacramento. However, until the 1960s, US 50 actually went beyond Sacramento: it continued down to Stockton, and then west over the Bay Bridge, ending in San Francisco. That was the "classic" version of US 50: a coast-to-nearly-coast route. So what was its mileage at that time, and where was its midpoint?
When US 50 went to San Francisco, it was 118 miles longer, for a total length of 3133 miles. Its midpoint, then, would have been at the 1566.5 mile mark. This was one mile east of Wright KS (which itself is just a few miles east of Dodge City).
The signs shown in these next photos (obviously not an official KDoT sign) was not claiming to be the midpoint of US 50 (since US 50 never went to New York), but it is interesting to note that this sign was posted 25 miles east of the midpoint that I calculated: