Back Porch Flat Roof Rotted Rafters and Plywood

My back porch (25’ x 15’) has had a small leak in one spot for close to a year. Recently, I peeled back the roofing paper and saw much more damage than I expected. The rafters extending out from the house appear to be 2”x8”s and the front rafter that runs parallel to the house that the rain gutter nails in to also appears to be 2”x8”. Some of the 2”x8”s extending from the house are rotted at the front, that is, about 25% is rotted and the other 75% is good wood. The front 2”x8” is badly rotted. To repair this, can I saw off the rot and bolt on new wood that is not rotted? Does the existing ceiling need to come out? For now, I need a quick an easy fix. Hope the pictures will help.

The front wood is called the fascia
And you will need to just remove and replace this wood.

The rafters, you cut a piece of wood and nail it to the side of it so your decking has something solid to nail into.

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What roof_lover said, but add some pics to help us help you better.