Comment that not enough information for Math #6 to be solved is in error.
Start at the end, last 15 minutes (at 45 minutes) require 20,000 lbs for payload but additional will be needed to carry weight of fuel. So 2 fuel rockets total needed at 45 minutes. 20,000 plus 20,000 fuel require 40,000 plus fuel needed to carry that load at 30 minutes to 45 minutes. Hence, 2 rockets plus 1 additional to carry the 2 fuel rockets plus 1 additional to carry the additional fuel rocket. So 4 fuel rockets needed from 30 minutes to 45 minutes. Same logic applies from 15 minutes to 30 minutes (yielding 8 rockets) and from 0 minutes to 15 minutes (yielding 16 rockets).
Add 16 + 8 + 4 + 2 = the grand total of 30 rockets.
