The way I understand what you're saying (which isn't too clear),
all he has to do is have 3 "foods" at the 40 point (end of day2);
then he takes all 3, eats one 40-60, one 60-80 and one 80-100.
There is a trip between A to B of 100km.
It is divided into 5 parts of 20 km each
A man needs to cover this distance
He can cover 20 km in each day
At A unlimited quantity of food is there
For every 20 km the man needs to take 1 food
the man can carry a maximum of three foods
he can drop the food in between the path wherever he likes
how will he reach the destination
Ok then, since you KNOW the answer:
I think your problem can be re-worded this way:
Jack needs to get from A to B, a distance of 100 km.
Jack can only walk 20 km each day.
At A is an unlimited number of water bottles.
Jack needs to drink one bottle of water for each 20 km.
And Jack can carry a maximum of only 3 bottles.
Jack may leave bottles at any spots from A to B.
How can Jack reach B ?
1: take 3 bottles, walk 20 km, leave one at 20 km, return : 2 days
2: repeat 3 more times: total 8 days (4 bottles at 20 km)
3: go to 20 km : total 9 days (6 bottles at 20 km)
4: repeat above for 3 days: total 12 days (3 bottles at 40 km)
5: walk the remaining 60 km, drinking 1 bottle each day: total 15 days.
That's a "quick" solution, since you did not specify MINIMUM.
If you do know how to solve this and you have posted this as a challenge to other member then this is where the question belongs.
However if you do not know how to solve this and are look for help in solving it then it is not a challenge problem as defined in this forums title.
The question is being asked of this problem because to the staff it looks like the latter rather than the former