Fireball casting speed

Oh oops. Thanks for checking my math. For #4, I was dividing, I just forgot to proofread.
Edit: Now I remember what happened. I made the assumption that the original cast speed is 100%. I treated increases to speed as adding onto that number. So a +40% speed wand would increase cast speed to 140%, or 1.4. After that, I took the inverse of that number to determine what percentage of the original cast time remains. I take that number, then multiply it by the unmodified cast time. It's a bit roundabout, yes, but it helps me to keep track of things. So what I have is

• 20/(1+(.4+.3)) = 20/1.7 = 11.765 (Way too many significant digits, yes.)
• 11.765/(1.4216) = 8.276

Using your formula, a wand with +36% cast speed (what I currently have on hand) should be

• 20*(1-0.36) = 20*0.64 = 12.8

With mine its

• 20/(1.36) = 14.705

Actually testing it results in 13 seconds, with an error of 1 second. I'd need more data to call it either way though. On a side note: Thanks for bringing to attention all of those assumptions. It's a fine night for a experiment.