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?

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

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