Mix the flour, salt and baking powder in a large bowl. Add the butter and shortening. Cut in the butter and shortening until the flour resembles cornmeal, using a fork or your hands. Add the water to the mixture a little at a time until the dough is soft and not sticky. Place the dough on a lightly floured surface and knead the dough for a few minutes until smooth and elastic. Divide the dough into 8 equal pieces and roll each piece into a ball. Let the dough balls rest, covered with a towel, about 15 minutes.
Preheat a large skillet over medium-high heat. Use a rolling pin to roll each dough ball into a thin 7-inch round tortilla. Place the tortillas one at a time into the skillet and cook until bubbly and golden, about 1 1/2 minutes. Flip the tortilla and continue cooking until golden on the other side. Put the cooked tortilla in a tortilla warmer or wrap in a clean kitchen towel. Repeat with the remaining dough.