In world 6-5, what is the pattern needed to get the time and path ribbons?

I'm going to number each room to make it easier. Starting in the first room where the mouse starts this will be room number one. So rooms 1-5 will be the first row, 6-10 the 2nd row and 11-15 the 3rd row. The pattern is as follows for both timing and path ribbons...

Room 1 to yellow door (only choice)
Room 7 to purple door. Wait long enough for the fat ghost cat to move then go through the purple door. If you are going for only 10 paths draw a couple of circles in the room before going through.

Room 8 to green door
Room 14 to orange door
Room 9 grab cheese and go back through the only door. (if you are going for only ten paths make sure you have only one path in and out of this room)
Room 14 back to green door
Room 8 to grey door
Room 13 grab cheese and go back out grey door
Room 4 to blue door
Room 12 to red door
Room 15 to finish.

The previous answer works fine for the :20 time ribbon, however, this method will actually give you 11 paths.

Using the same room numbering scheme to achieve 10 paths:

Room 1 Yellow - Room 10 Yellow
Room 10 Grey (becomes Green) - Room 14 Green
Room 14 Orange - Room 9 Orange (Get cheese and back through same door in one path)
Room 9 Orange - Room 14 Orange (Circle this room a few times to draw room 8 cat to you)
Room 14 Green - Room 8 Green
Room 8 Grey - Room 13 Grey (Get cheese and back through same door in one path)
Room 13 Grey - Room 4 Grey
Room 4 Blue - Room 12 Blue
Room 12 Red - Room 15 Red
Room 15 - Door

Hope this helps