We found the fastest two solutions-
Answer I involved the quickest walker carrying the torch with each of the others in turn and running back. This took 21mins.
Answer II involved the slowest two walking together for the middle journey, with the quicker runners going over together first and carrying the torch back. This took 17 minutes.
We wondered if answer II would always be quicker if the walkers had different speeds, so we named them a, b, c and d and broke it down like this:
Journey times : a < b < c < d
Answer I: b+a+c+a+d =2a + b + c + d
Answer II: b+b+d+a+b = a + 3b + d
We spotted that Answer II was usually quicker, but it had more "b's" in it, so we create a problem where b was high-
a= 1 min
b = 20mins
c = 21mins
d = 22mins
This makes answer I nearly 20 minutes quicker!
(If you make a-d the numbers 1-4 then both answers take 11 minutes)