Given
climber starts with 25 oxygen canisters
we need to find minimum possible time to climb 10 kms to summit.
we know that, total climb time = Time spent climbing and Time spent stopping (if a stop needed for oxygen)
condition : stopping always adds exactly 25 mins to total climb time
lets consider climber have enoigh oxygen for 10 km climb at each pace.
slower pace : uses 2 canisters per km
so total canister needed = 10km * 2 = 20
Here we can observe that
no stop is requiredfaster pace : uses 30% oxygen than slower pace
oxygen per km = 2 + (20*30/100) = 2 + 0.6 = 2.6
total canister needed = 10km * 2.6 = 26 canisters
Here we con observe that climber has 25 only , we need 1 more canister. Therefore,
stop is requiredNow lets calculate total time for each pace, we know that distance = speed * time
slower pace : (4 kmph) with
no stopClimbing time = 10km /4kmph = 2.5 hours = 2.5 * 60 mins = 25 * 6=
150 mins ----->condition 1
faster pace : ( 5kmph) with 1 stop
climbing time = 10 km / 5kmph = 2 hours = 2 * 60mins = 120 mins
as per condition stopping always adds 25 mins, so total climbing time = 120 + 25 =
145 mins -----> condition 2
Therefor by comparing, condition1 and condition2, the minimum possible time to reach the summit = 145 mins