#### mineshaft maths

Re. the mineshaft maths question, from my back-of-the-envelope calculation (no calculator, I'm 46), I reckon

the circumference of the drum is pi.d where d = 0.7

it rotates at 10 rpm so the cage moves at 10.pi.d m/min = 7.pi m/min

To rescue 21 people 10 at a time it needs to go down and up 3 times = 6 journeys

each journey is 22m, so the total distance is 6.22 m

it needs to be loaded 3 times and unloaded 3 times = 6 times

each load/unload takes 10 seconds, so loading takes 6 x 10 seconds = 1 minute

total time is (6.22 m)/(7.pi m/min) + 1 minutes

22/7 = pi (give or take) so the answer's 'about seven minutes'.