Shouldn't your formula be ((H-(A-B)/(A-B))? Or more clearly, letting d be the progress per day (A-B): ((H-d)/d)+1.

Question

Not a question, but a comment on Shobikaj's formula for the snail's journey.

Answer 1

the simplest form for the equation is literally distance = rate * time. we know distance and we know rate. distance / rate = time. the only caveat here is the wording. does reach the top mean attain that height or have his final end of day height be at the top of the tree. because he will reach it the top on day 2 but then slide back down 1m. on day 3 he will try to go up 2m but only be 1m down from top of tree.

so depending on how you look at it you have 2 options:
t = h / d
or
t = (h / d) - 1

Answer 2

Very educational. Thank you. I really had forgotten about the physics courses I have under my belt.
One question though...How can the equation to use be
days=H/d
or
days=(H/d) -1
or
days=((H-d)/d)+1
???
I, very much, hope that your answer does not suggest that it is 'because we live in a great big, beautiful universe'.

Answer 3

distance (meters) = rate (meters/day) * time (days)
distance / rate gives us units of days as meters / (meters/day) becomes (meters/1) * (days/meters) and meters cancel. what letters you use aren't really important as long as the units are consistent and they are.

My actual background of study was astrophysics. Programming was just a hobby. not it's my career and physics is the hobby.