When cooking a 3-pound beef roast in a crock pot on the low setting, you can generally expect it to take around 8 to 10 hours to become tender and fully cooked. Slow cooking allows the meat to become fork-tender and develop rich flavors over an extended period.
Keep in mind that cooking times may vary based on factors such as the specific cut of beef, the crock pot's model and size, and your desired level of doneness. It's always a good idea to use a meat thermometer to ensure the roast reaches a safe internal temperature. For beef, the USDA recommends an internal temperature of at least 145°F (63°C) for medium-rare and 160°F (71°C) for medium.
Also, if your crock pot has a temperature probe, you can insert it into the thickest part of the roast to monitor the internal temperature as it cooks.
If you want to speed up the cooking time, you can set the crock pot to the high setting, but keep in mind that the texture and flavors might not be as developed as with a longer, slower cooking time. Slow cooking on low heat is often preferred for achieving the best results with a beef roast.