Fish can go a surprisingly long time without food. Mammals like us need quite a lot of food, often, because we have to generate our own body heat, and that requires a lot of energy. Fish take their body temperature from the water they're in, so they can manage for a long time without food - but it feels alien to us because we don't want to imagine them being hungry, and they always act hungry! lol. The tanks will have algae and microcritters in them that many of the fish will pick at too, I would make sure the substrate is clean and do a lot of water changes before going, but leave the tank glass alone so algae can grow that they can pick at while you're away. Adding things like almond leaves and alder cones will also attract and grow micro critters like seed shrimp that lots of fish will eat.
A week is fine, even two weeks. Some would say three weeks is okay, and it probably would be, but in your shoes, if the person can be trusted, I'd portion out a meal in a ziplock back for each tank, taped to the tank it's for.
Have them feed each tank once or twice at most while you're away, hide the food containers, and stress to them how crucial it is not to feed them any more than the portion you've given them, or it risks making the water toxic and killing the fish while you're gone.