A firefighter stood on the middle rungs of a ladder ,spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs.After some minutes he was able to climb 18 rungs to the very top of ladder .How many rungs did the ladder have ?
Please, help me out this more clearly.Thank a lot.
72738r
Let M = middle rung
M + 6 - 10 + 18
M + 14 = top of ladder
14 + 14 = ?
Very good
To solve this problem, let's break it down step by step:
1. Initially, the firefighter is standing on the middle rungs of the ladder and spraying water on the burning house.
2. He then climbs up 6 rungs, but the heat of the flames forces him to come down 10 rungs.
3. After some time, he is able to climb 18 rungs to reach the very top of the ladder.
Now, let's find the total number of rungs in the ladder.
Let's assume that there are 'x' total rungs in the ladder.
1. Initially, the firefighter is on the middle rungs. Considering there are 'x' total rungs, the number of rungs he climbed up can be represented as (x/2).
2. He then climbs up 6 rungs, so the number of rungs he climbed up now becomes (x/2) + 6.
3. However, the heat of the flames forces him to come down 10 rungs, so the number of rungs he climbed up now becomes (x/2) + 6 - 10.
4. After some time, he manages to climb 18 rungs to reach the top, so the number of rungs he climbed up now becomes (x/2) + 6 - 10 + 18.
Now, we know that the final number of rungs he climbed up is equal to the total number of rungs 'x'. So we can set up the equation:
(x/2) + 6 - 10 + 18 = x.
Simplifying this equation, we get:
(x + 12)/2 = x.
Cross-multiplying, we get:
x + 12 = 2x.
Subtracting 'x' from both sides, we get:
12 = x.
Therefore, the ladder has 12 rungs in total.
So, the ladder has 12 rungs.