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12 Jan 2026, 06:04
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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
A. 120 minutes
B. 140 minutes
C. 145 minutes
D. 150 minutes
E. 175 minutes
12 Jan 2026, 06:04
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Official Solution:
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
Case 1: Slower pace
Speed = 4 km/hour
Time = 10 km/4 = 2.5 hours = 150 minutes
Oxygen use = 2 canisters per km
Total needed = 10 * 2 = 20 canisters
He has 25, so no stop needed
Total time = 150 minutes
Case 2: Faster pace
Speed = 5 km/hour
Time = 10 km/5 = 2 hours = 120 minutes
Oxygen use = 30 percent more than 2, so 2.6 canisters per km
Total needed = 10 * 2.6 = 26 canisters
He has only 25, so he must stop
Stop adds 25 minutes
Total time = 120 + 25 = 145 minutes
Answer: C
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
Case 1: Slower pace
Speed = 4 km/hour
Time = 10 km/4 = 2.5 hours = 150 minutes
Oxygen use = 2 canisters per km
Total needed = 10 * 2 = 20 canisters
He has 25, so no stop needed
Total time = 150 minutes
Case 2: Faster pace
Speed = 5 km/hour
Time = 10 km/5 = 2 hours = 120 minutes
Oxygen use = 30 percent more than 2, so 2.6 canisters per km
Total needed = 10 * 2.6 = 26 canisters
He has only 25, so he must stop
Stop adds 25 minutes
Total time = 120 + 25 = 145 minutes
Answer: C
