Caluclate average depending on number of instances on each line - Bash - AWK

How can you work out the average on each line when each row has a variation on the number of alphanumeric instances including a final total average?

ie. pie.txt:

0.8pie 0.7pie 0.6pie            
34.2pie 34.1pie 35.8pie 
42pie 43pie 43pie
44pie 41pie 38pie
0.8pie
34.2pie 34.1pie
42pie 43pie 43.0pie
44.1pie 41pie 38.7pie 58.2pie

Desired Output:

Instances of Pie:               Avg:
0.8pie 0.7pie 0.6pie            Avg pie:  1.7pie
34.2pie 34.1pie 35.8pie         Avg pie:  34.7pie
42pie 43pie 43pie               Avg pie:  42.7pie
44pie 41pie 38pie               Avg pie:  41pie
0.8pie                          Avg pie:  0.8pie
34.2pie 34.1pie                 Avg pie:  34.15pie
42pie 43pie 43.0pie             Avg pie:  42.7pie
44.1pie 41pie 38.7pie 58.2pie   Avg pie:  45.5pie

Total Average:                            30.41pie

If there was always a set amount on each line like 2 or lets say 3 pies then yeah I can easily utilise awk print ($1+$2+$3)/3 etc. But I'm struggling when there is a variance on each line.

I would imagine the use of conditional statements to determine the number on each line. ie. If row one has 3 then divide by 3, if row two has 4 then divide by 4 etc.

Can anyone kindly assist?