In one oven I need to bake 2 dishes: one needs 35 minutes at 375ºF, and the other needs 45 minutes at 350ºF. How much time should the second dish cook at 375ºF?
On a practical basis? 40 to 45 min. That is, bake it for 40 min and then check it to see if it's done (or otherwise check it 5 minutes earlier than you otherwise would).
The difference between 350F and 375F in actual cooking is generally dwarfed by the temperature inaccuracy of home ovens.
To be honest, your probably don't even need to worry about the slightly different timing and temperatures.
I'm not a temperature expert but, I'm relatively sure that Fahrenheit should be converted to Kelvin to calculate the specific difference between two temperatures. 25F sounds like a big difference but it really isn't.
350f = 449.817 kelvin
375f = 463.706 kelvin
Then we can compare the values:
449.817/463.706 = 0.97
This shows us there's a 3% actual difference.
If you wanted to figure out the precise timing (but i assure you it won't matter) - you'd calculate 97% of the longer time which ends up being 43 minutes and 39 seconds.
I'm fairly sure if 1 minute and 21 seconds longer is going to ruin your dish - you're doing something else wrong.