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?
you are finding how many steps are from the middle to each end of the ladder so you have 2n. next you know the middle step is going to count as 1 so you have the equation 2n + 1
up 6 down 10 up 18
6 - 10 +18 =14
2n + 1
2 (14) + 1
28 + 1
29 steps
Let R = rungs
.5R + 6 - 10 + 18 = R
Solve for R.
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 ,answer clearly because I'm want to explain for my son how to solve the problem.Thanhs a lot.
To determine the number of rungs on the ladder, we can follow the steps outlined in the problem.
1. The firefighter starts on the middle rungs of the ladder.
2. He then climbs up 6 rungs.
3. The heat forces him to come down 10 rungs.
4. After some time, he is able to climb 18 rungs to reach the top of the ladder.
Let's use algebra to solve this problem. Let's assume the number of rungs on the ladder is "x".
From the problem, we can write the following equations:
1. The firefighter climbs up 6 rungs: x/2 + 6
2. He comes down 10 rungs: (x/2 + 6) - 10
3. He is able to climb 18 rungs: [(x/2 + 6) - 10] + 18
To solve for x, we can equate the third equation to x:
(x/2 + 6) - 10 + 18 = x
We can simplify and solve this equation:
x/2 - 10 + 24 = x
x/2 + 14 = x
14 = x - x/2
14 = (2x - x)/2
14 = x/2
28 = x
Therefore, the ladder has 28 rungs.