a fireman stood on the middle step of a ladder, shooting water into a burning building, as the smoke lessened, he climbed up 3 steps, and continued his work, the fire got worse, so he had to go down 5 steps, later he climbed up the last 6 steps and was at the top of the ladder. how many steps were there?
3 - 5 + 6 = 4
The middle step must be step 4.
Let's break down the steps of the fireman's actions to determine how many steps were on the ladder.
1. The fireman starts on the middle step of the ladder.
2. He climbs up 3 steps.
3. He goes down 5 steps.
4. Finally, he climbs up the last 6 steps to reach the top of the ladder.
To find the total number of steps on the ladder, we can calculate the net change in the fireman's position.
Starting from the middle step, he first climbs up 3 steps (+3), then goes down 5 steps (-5), and finally climbs up the last 6 steps (+6).
So the net change in his position is +3 - 5 + 6 = +4 steps.
Since the net change in position is +4 steps, we can deduce that the ladder had a total of 4 steps.
Therefore, there were 4 steps on the ladder.
To solve this problem, let's break it down step by step:
1. Let's assume the number of steps on the ladder is 'N'.
2. Initially, the fireman stood on the middle step, so he was on step (N / 2) + 1 (as there is no step 0).
3. He then climbed up 3 steps, which means his new position was (N / 2) + 1 + 3 = (N / 2) + 4.
4. Later, he had to go down 5 steps, which means his position became (N / 2) + 4 - 5 = (N / 2) - 1.
5. Finally, the fireman climbed up the last 6 steps to reach the top, which means his final position was (N / 2) - 1 + 6 = (N / 2) + 5.
6. Since his final position is at the top of the ladder, we can equate it to the total number of steps, N.
(N / 2) + 5 = N
7. To solve for N, we can multiply both sides of the equation by 2:
2 * ((N / 2) + 5) = 2 * N
N + 10 = 2N
8. Subtracting N from both sides gives us:
10 = N
Therefore, there were 10 steps on the ladder.