I own 1 1993 Honda Accord and after about 10-15 minutes of driving the engine will completely stop and the "check engine" light will come on. If I wait about 10 minutes or so it will start back up and go for about the same amount of time. Does anyone know what the problem could be?

First, when your car is a no-start, test for loss of spark.
You're likely losing spark due to an overheating of the Ignition Control Module (ICM) located in the distributor. These components break down due to time and heat.
If your's hasn't been replaced recently or since the vehicle was new, now would be the time.
Let us know...

Yes, replacing the Ignition Control Module (ICM) and coil should solve your problem:

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