Air conditioner won’t keep up? What could be the issue?

My mother and I just moved into our grandmother’s house. Since we moved in, we noticed our grandma’s AC unit runs constantly. It has only been 80 degrees each day we’ve been here, and her house is medium-sized, but we noticed her air conditioner won’t keep up. It’s set at 72, but during the hottest part of the day,... show more My mother and I just moved into our grandmother’s house. Since we moved in, we noticed our grandma’s AC unit runs constantly. It has only been 80 degrees each day we’ve been here, and her house is medium-sized, but we noticed her air conditioner won’t keep up. It’s set at 72, but during the hottest part of the day, the thermostat will register 78-79 and keep running.

Once the sun goes down, it is able to catch up and hit 72 and shut off. What could be the cause of the lag? The unit is 27 years old, so we’re wondering if it may need replaced soon. The AC guy is coming tomorrow.
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