Amy is just learning how to rock climb. Her instructor takes her to a 26 ft climbing wall for her first time. She climbs up 5 ft in 2 min. But then slips back 2 ft in 10 sec. This pattern (up 5 feet down 2 ft) continues until she reaches the top. How long will it take her to reach the very top?

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Mathematics

10 May, 07:54

Amy is just learning how to rock climb. Her instructor takes her to a 26 ft climbing wall for her first time. She climbs up 5 ft in 2 min. But then slips back 2 ft in 10 sec. This pattern (up 5 feet down 2 ft) continues until she reaches the top. How long will it take her to reach the very top?

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Natalia · Answer 1

Let's compute the speeds as she goes up and down of the climbing wall. Speed is the ratio of distance to time.

Speed going up = 5 ft / (2min * 60 s/1 min) = 1/24 ft/s

Speed going down = 2 ft/10 s = 0.2 ft/s

Net speed = 1/24 ft/s - 0.2 ft/s = 5/24 ft/s

Using this net speed, we can already calculate for the total time:

Speed = Distance/Time

5/24 ft/s = 26 ft/Time

Time = 124.8 seconds or 2.08 minutes