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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 required

faster 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 required

Now lets calculate total time for each pace, we know that distance = speed * time

slower pace : (4 kmph) with no stop
Climbing 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
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Slower pace = 10/4= 2.5 hrs = 2.5x60= 150 minutes
Faster pace= 10/5= 2hrs x60+25= 145 minutes
Hence C
Bunuel
A mountain climber is 10 kilometers from the summit and carries 25 oxygen canisters. The climber can climb at one of two constant paces. At the slower pace, the climber gains 4 kilometers per hour and uses 2 oxygen canisters per kilometer. At the faster pace, the climber gains 5 kilometers per hour but uses 30 percent more oxygen to climb any given distance than at the slower pace. Along the route, there is a single stopping point where the climber may pick up extra canisters. Stopping there always adds exactly 25 minutes to the total climb time, regardless of how many canisters are taken. The climber must choose either the slower pace or the faster pace and maintain that pace for the entire climb. What is the minimum possible time, in minutes, needed for the climber to reach the summit?

A. 120 minutes
B. 140 minutes
C. 145 minutes
D. 150 minutes
E. 175 minutes

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Slower pace is 4 km / hr using 8 cylinders (2 cylinder / km).
Total time taken with slow pace = Distance / Speed, i.e. 10 / 4 = 2.5 hours or 150 min

Walking at 5 km / hr will consume 30% more oxygen, i.e. 2.6 cylinder / km.
For a total distance of 10 km, 26 cylinders would be needed against the availability of 25 cylinders. Hence, a stop of 25 mins would have to be made.
Total time with faster pace = Distance / Speed + Extra time for refilling cylinder
(10 / 5) hrs + 25 mins = 2 hours 25 mins or 145 mins

Hence, 145 mins would be the least time needed to make the summit.
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Slow speed data
Speed- 4 k/h
Use - 2 can /hr
Time- 600/4- 150 min
Can used- 20
No need of any more
So no additional 25 min

Faster speed data
Speed- 5k/h
Use -2.6 can / hr
Can used -26
So we need to stop to get more
Time- 600/5 -120 min
Add 25 min .
Total- 145 min
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Total canisters that climber is carrying are 25.
Through slow pace:
canisters used is 2 for each KM. So, total of 10*2 = 20
and time time taken for 10 KM will be 150 mins as 4 KM is getting covered in 60 mins.
Through fast pace:
canisters used for each KM = 2 * 1.30 = 2.6 canisters
Total canisters for 10 KM = 10* 2.6 = 26 canisters
As total canisters climber is carrying is 25 only. He needs to stop for 25 mins
Time taken to cover 10 KM will be 120 mins as 5 KM is getting covered in 60 mins.
Total time = Distance covered + Stoppage time
= 120+25 = 145 mins

So, answer is C through fast pace minimum time will be 145 mins
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Slow:
10 km can be covered in 2.5 hrs
2*10=20 cylinders reqd. so additional cylinder not required.
thus total time = 150 min

fast:
10km can be covered in 2 hrs
cylinder reqd = 2*10*1.3=26
so additional cylinder reqd. so break of 25 min required
total time =120+25 =145 min

Ans C
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There are 2 constant paces option -

Slow Pace: covers 4 km/hr and uses 2 oxygen canisters per km

Fast Pace: covers 5 km/hr and uses 30% more oxygen canisters per km = 2*1.3 = 2.6 oxygen canisters per km

Total distance to be covered = 10 km
Total oxygen canisters available to climber = 25

At stopping point, climber can pick extra canisters, with addition of 25 minutes in travel time.

If the climber chooses slower pace, time needed = distance/speed = 410/4 = 2.5 hours = 150 minutes
canisters needed = distance (in km) * canisters required per km = 10 * 2 = 20 canisters.
Since, the climber has 25 when he started, this is enough.

If the climber chooses fast pace, time needed = 10/5 = 2 hours = 120 minutes
canisters needed = 10*2.6 = 26 canisters
Since he started with 25, he needs one more. So, he needs to stop at the stopping point, which will add 25 extra minutes in total travel time, making it to 145 minutes (120+25).

Therefore, out of the 2 options, the minimum time required is 145 minutes.

Hence, (C) is the answer
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Let's calculuate how much oxygen and time the climber will spend in two scenarios.

(1) Slower pace
\(t = 10/4 = 2.5\) hours, or 150 minutes.
\(x = 2*10 = 20 \) oxygen canisters
So, there's enough oxygen to manage.

(2) Quicker pace
\(t = 10/5 = 2\) hours
\(x=2*10*1.3 = 26 \) canisters
One canister is lacking, so the climber would have to make a pit-stop
Therefore, final time \(t=120 + 25 = 145\) minutes.

Even with the stop, the second scenario is faster. The right answer is C.
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At slower pace, speed = 4km/hr & 2 canister/km
total time taken to cover 10kms = 2.5 hrs and oxygen canisters used = 20

At faster pace, speed = 5kms/hr & 30% more oxygen used, hence canister used = 2*1.3 = 2.6 canister/km
total time taken to cover 10kms = 2hrs, oxygen canisters used = 26, which means he will have to stop for 25mins to get extra canister hence total time at faster pace is 2hrs 25mins.

Hence he will go at faster pace and minimum time is 145mins

And C
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Bunuel
A mountain climber is 10 kilometers from the summit and carries 25 oxygen canisters. The climber can climb at one of two constant paces. At the slower pace, the climber gains 4 kilometers per hour and uses 2 oxygen canisters per kilometer. At the faster pace, the climber gains 5 kilometers per hour but uses 30 percent more oxygen to climb any given distance than at the slower pace. Along the route, there is a single stopping point where the climber may pick up extra canisters. Stopping there always adds exactly 25 minutes to the total climb time, regardless of how many canisters are taken. The climber must choose either the slower pace or the faster pace and maintain that pace for the entire climb. What is the minimum possible time, in minutes, needed for the climber to reach the summit?

A. 120 minutes
B. 140 minutes
C. 145 minutes
D. 150 minutes
E. 175 minutes

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Total distance he should cover: 10km , Total Oxy canister available: 25

a) Slow Pace: 4km/hr , consume 2 Oxy Canister
so to cover 10km distance --> he would take 2hr 30mins (1st hr 4km covered, 2nd hr 4km covered, next half hour 2km covered) + 25 minutes stop time
so total time consumed with slow pace is 2hr 55mins (175 mins)

b) Fast Pace: 5km/hr , consume 30% oxy more than 2 Oxy/km
so to cover 10km distance --> he would take 2hr (1st hr 5km covered , 2nd hr 5km covered) + 25 minutes stop time
so total time consumed with fast pace is 2hr 25mins (145mins)

Hence he will choose fast pace to cover 10km in 145mins
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Minimum possible time can be achieved when speed is maximum.

Max speed = 5 km/hr , Time = 10km / 5km/r = 2hr =120mins
Now the canister required every km = 2, when speed= 4km / hr
the canister required every km = 2.6 (30% more), when speed maximum = 5km /hr
So, number of canisters required are: 2.6*10 = 26
A the climber only has 25 cans, and he has to stop to get more for additional 25mins
So total time required: 120+25 = 145mins
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Total distance to climb : 10kms

At slower pace :climber travels 4kms / hr
Hence time taken will be 10/4 = 2.5 hours = 150 mins
Climber uses 2 Canisters/km = 2 *10 = 20 Canisters
Since , he is carrying 25 Canisters, no need for extra Canisters and no stopping is required.
Hence total time taken at slower pace = 150 mins

At faster pace i.e. 5 kms per hour climber will take 10/5 = 2 hours =120 mins
But, climber uses 30% more oxygen i.e. 2 * 1.3 = 2.6 canisters/km
Hence will require 2.6*10 = 26 Canisters.
But as he is carrying 25, for extra Canisters he will take a stop of 25 mins in addition.
So total time taken at faster pace = 120 + 25 =145 mins
Hence , minimum possible time to reach the summit is 145 mins.
Hence option C.
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In both options we have to travel 10km, and have 25 Oxygen containers (OX)

Speed 1) 10KM/4 KMH = 2.5 hrs climb time | 2 OX per KM tells us to multiply so 2 OX * 10km is 20 OX | 25 OX - 20 OX = 5 OX | No stop is needed

Minimum time so far is 60*2.5 or 150 minutes

Speed 2) 10KM / 5 KMH = 2 hours climb time | 30% more oxygen to climb any distance than option 1 | option one takes 20 OX so 20 OX * 1.3 = 26 OX required | 25 OX starting - 26 Req. = -1 OX A stop is needed

2 hours climb time + 25 minutes stop = 2*60 + 25 = 120+25 =145 minutes to reach summit

Answer) option C


Bunuel
A mountain climber is 10 kilometers from the summit and carries 25 oxygen canisters. The climber can climb at one of two constant paces. At the slower pace, the climber gains 4 kilometers per hour and uses 2 oxygen canisters per kilometer. At the faster pace, the climber gains 5 kilometers per hour but uses 30 percent more oxygen to climb any given distance than at the slower pace. Along the route, there is a single stopping point where the climber may pick up extra canisters. Stopping there always adds exactly 25 minutes to the total climb time, regardless of how many canisters are taken. The climber must choose either the slower pace or the faster pace and maintain that pace for the entire climb. What is the minimum possible time, in minutes, needed for the climber to reach the summit?

A. 120 minutes
B. 140 minutes
C. 145 minutes
D. 150 minutes
E. 175 minutes

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I got 145 minutes.

At a slower pace, the climber moves at 4km/h and uses 2 canisters/jm, so for 10km that is 20 canisters total, which is within the 25 they have. That means no stop is needed and total time is 10/4=2.5 hours, 150 minutes.

At the faster pace, the climber goes 5km/ h but uses 30% more oxygen, 10x2.6=26 canisters needed. The only have 25 so they'd have to stop once for more, adding 25 minutes. The climb itself takes 10/5= 2 hours = 120 minutes and whit the stop, 145 minutes.

So the faster pace ends up being quicker 145 minutes.

I ran out of time, so I guessed 145 towards the end because when a problem adds a fixed time like 25 minutes, it breaks the clean multiple of 10 pattern you'd get from even speeds or rates.

So while 4km/h gives 150 mins, which ends in 0, adding 25 to 120 min naturally gives 145, totals with offsets like 15 or 25 almost always end in 5, not 0.
Bunuel
A mountain climber is 10 kilometers from the summit and carries 25 oxygen canisters. The climber can climb at one of two constant paces. At the slower pace, the climber gains 4 kilometers per hour and uses 2 oxygen canisters per kilometer. At the faster pace, the climber gains 5 kilometers per hour but uses 30 percent more oxygen to climb any given distance than at the slower pace. Along the route, there is a single stopping point where the climber may pick up extra canisters. Stopping there always adds exactly 25 minutes to the total climb time, regardless of how many canisters are taken. The climber must choose either the slower pace or the faster pace and maintain that pace for the entire climb. What is the minimum possible time, in minutes, needed for the climber to reach the summit?

A. 120 minutes
B. 140 minutes
C. 145 minutes
D. 150 minutes
E. 175 minutes

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At the slower pace the climber has enough oxygen canisters without needing to stop because he would use 2*10=20 canisters.
He would take 10/4 = 2.5 hours = 150 minutes.

At the faster pace the climber doesn't have enough oxygen canisters because he would use 2*10*1.3=26 canisters and he has only 25.
He needs to stop -> 25 extra minutes.
He would take 10/5 * 60 + 25 = 120 + 25 = 145 minutes.

Minimum possible time = 145 minutes

IMO C
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The constraint is the number of oxygen canisters. The climber has 25:

Slower pace: 2 * 10 = 20, sufficient
Faster pace: 20 * (1 + 30/100) = 26, insufficient

The time needed:

Slower pace: 60 * 10/4 = 150 minutes
Faster pace: 60 * 10/5 + 25(stop) = 145 minutes

145<150, so 145 minutes is the answer

Answer C
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1. Analyze the oxygen requirements
Climber starts with 25 canisters and needs to cover 10 km.

1st Option : Slower pace
2 canister/ km , Hence total needed = 10 km *2 = 20 canisters
and since 20 is less than 25 , the climber can finish without stopping.

2nd Option: Faster Pace
Uses 30% more oxygen than slower pace
Consumption = 2*1.3 = 2.6 Canisters/km
Total needed = 10 km * 2.6 = 26 canisters
Since 26 is more than 25 canister carried, the climber must stop to pick up extra canisters.

2. Calculate the total time for each pace

1st Option : Slower pace
Time = Distance /Speed = 10/ 4 = 2.5 hours
Convert to minutes = 2.5*60= 150 minutes

2nd Option : Faster pace
Time = Distance/ Speed = 10/5 = 2 hours = 120 minutes
Penalty for mandatory oxygen stop = 25 minutes
Total time = 120+25= 145 minutes

Hence
Options 2 gives less time = 145 minutes
Answer C
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