Odometer (correct) = Odometer (indicated)/0.9.
For example, if 1.0 miles actually traveled by the car results in 0.9 miles being indicated on the odometer, then using the above formula results in:
Odometer (correct) = 0.9 miles/0.9 = 1.0 miles. Similarly, 52.5 miles indicated = 52.5 miles/0.9 = 58.3 miles actual.
As stated above, while the odometer is direct drive, the speed indication comes from a rotating magnet acting on a spring-loaded speed dial. Thus, the faster the driveshaft turns, the faster the speedometer cable turns, the faster the magnet in the speedometer turns, the greater the influence of the spinning magnet on the spring-loaded speed dial, the more the speed dial is displaced, and the higher the indicated speed.
At least that’s the way it’s supposed to work.
So, PRESUMING there is a 1-to-1 correspondence between the “effective” magnetic field created at various speeds and the odometer reading (that is, presuming there is a linear relationship between the indirect-drive speed indication and the direct-drive odometer), then the above relationship should also suffice; that is:
Speed (correct) = Speed (indicated)/0.9.
Or, to use the example posed in the question:
Speed (correct) = 50 mph/0.9 = 55.6 mph.
However, I would be leery of presuming any linear relationship between the odometer and speedometer. As an example, if the speed dial spring were broken or the speed dial shaft were frozen in its pivots, then there would be no linear relationship between the indicated speed and indicated/actual distance traveled (unless you consider "whatever speed/distance = 0 mph or 0 miles" to be linear).
So, absent the very handy (and exceedingly accurate) GPS solution suggested above, I would head back to the road with a stop watch and – maintaining constant speeds such as 25 mph, 40 mph and 55 mph (for example) – compare the indicated and actual speeds for set distances (you can use the roadside mileage markers).
Then you could, if desired, create a table of indicated vs. actual speeds. This is what I did for the otherwise-nicely-operating speedometer in my 1930 coupe, having found that the actual speed was about 2 mph slower at 20 mph, up to 3 mph slower at 55 mph (which in and of itself, points to some non-linearity in the indicated speed).
Of course, all this should be done with the assistance of your faithful companion and not attempted (as some of us may be inclined to do) by yourself. Besides the obvious advantage of accuracy, there are some of us who find it difficult to stay in the center of our lane at a safe distance from surrounding traffic in the normal course of driving, much less while attempting to maintain a constant speed, operate a stopwatch, record the speedometer readings and keep track of the roadway mileage markers.
Ask me how I know…