Question

A firefighter is standing in front of a 24 step ladder. Every minute he climbs 4 steps and then the next minute he climbs down 3 steps. If he starts at 9:00, what time will he first step on the top rung of the ladder

Answer 1

After 2 minutes, he'll have climbed up 1 step. After 2k minutes, he'll have climbed up k steps.

Let's be careful, however, not to get to 24 -- at which point we should be done -- and then go back down 3 steps.

At 2(20) minutes, he is at step 20. That means, at 2(20)-1 minutes, he was at step 23. He was almost there, but then moved down 3 steps. However, now that he is at step 20 at 2(20) minutes, his next move is to climb up 4 steps, so he goes from step 20 to step 20+4=24. He's done. That means, at time 2(20)+1 minutes, he's done.

41 minutes after 9:00, he's finished, or 9:41.