Part 1 already solved by soot...

PART 1:
-you are standing next to a pile of Spam cans
-these are sufficient in number to complete this puzzle!
-you wish to walk a distance of 100 miles (straight path)
-you can walk 20 miles per day
-to keep up your strength, you need to eat a Spam can per mile
-you can carry 60 cans, no more
How long (minimum) will it take you to reach your destination
if you can hide cans at points 20, 40, 60 and 80 only?
PART 2:
Ok; that was easy: just a warmup, right?
This time, you can hide your cans anywhere you want.
What is the minimum number of cans you need in order
to reach your destination?
Caution: you cannot hide a part-Spam-can anywhere: too many ants.

OK; possible with 240 cans; this way:

-as with part 1, you want 120 at point 20, then 60 at point 40
-can be done with 240 cans by first taking 170 to point 10
-you need to eat 70: 240 - 20 - 20 - 20 - 10 = 170
-then eat 50; to point 20: 170 - 20 - 20 - 10 = 120
(then proceed as in part 1)

HOWEVER:
-can be done with 236 cans

How?

Before I forget it, here's solution:

-can be done with 236 cans, first using point 8 (then point 20)
-you need to eat 56: 236 - 16 - 16 - 16 - 8 = 180
-then eat 60; to point 20: 180 - 24 - 24 - 12 = 120
(then proceed as in 1st puzzle)
-since you need 20 cans per day, then time is 236 / 20 = 11 4/5 days.