In a large bowl, mix together the flour, salt, and 3 tablespoons of the sugar. Cut in the shortening until the mixture is crumbly and then add in the water to form a soft dough. Mix the dough until it holds together without crumbling.
Slice the apples into thin slices and place in a medium bowl with the remaining sugar, cornstarch, and the lemon juice. Let this mixture set for about 5 minutes.
Take the dough and divide it in half, place half of the dough into a greased tart dish or a cake pan. Use your fingers to stretch the dough over the bottom of the pans and about ½ inch up the sides. Repeat in a second pan for the rest of the dough.
Drain the apples from the juice in their bowl and arrange them in a pattern over the top of the dough with the blackberries. Place the tart in the oven at 400 degrees and bake for 35 to 45 minutes or until the crust is a golden brown.