A fireman stood on the middle step of a ladder, shooting water into a burning building . As the smoke lessened, he climbed up three steps and continued his work. the fire got worse,so he had to go down five steps. Later he climbed up the last six steps and was at the top of the ladder. How many steps were there?
7 steps
Let's break down the steps to solve this problem. We'll start by assigning variables to the unknowns.
Let's say the number of steps in the ladder is represented by 'x'. Since the fireman initially stood on the middle step, if we assume there are an odd number of steps, the middle step would be (x + 1) / 2. Let's represent the step number where the fireman initially stood as 'n'.
Based on the given information, we can state the following:
1. The fireman initially stood on the middle step (n = (x + 1) / 2).
2. He climbed up three steps and continued his work (n + 3).
3. The fire worsened, so he had to go down five steps (n + 3 - 5).
4. He later climbed up the last six steps and reached the top (x = n + 3 - 5 + 6).
We can now substitute the value of 'n' from the first equation into the last equation:
x = n + 3 - 5 + 6
x = [(x + 1) / 2] + 3 - 5 + 6
We'll solve the equation to find the value of 'x'.
2x = (x + 1) + 12 - 10
Simplifying, we get:
2x = x + 3
Subtracting 'x' from both sides:
x = 3
Therefore, the ladder has 3 steps.