Reply
Wed 13 Jun, 2007 10:29 am
A firefighter stood on the middle rung 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 the ladder. How many rungs did the ladder have?
1) The ladder has a middle rung. That means there is an odd number of rungs. Let N be the number of rungs. We will use 1-based indexing.
2) He starts on the middle rung, M. That means
M = (N+1)/2
3) Starting from the middle rung, he climbs up 6, down 10, up 18, and this leaves him on the top rung.
M + 6 - 10 + 18 = N
Solve:
M = N - 14
N-14 = (N+1)/2
N+1 = 2N - 28
N = 2N - 29
N = 29
There are 29 rungs. He started on the 15th rung.
29 is the answer I kept coming up with. I just didn't have a formula. I drew it out. I just wan't sure of my self. Thank you.
Re: Having a hard time.
mdgtbilly wrote:A firefighter stood on the middle rung 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 the ladder. How many rungs did the ladder have?
D D D peoples its not 29 duh thats dumb ok heres why
if your in the middle and you climb up 6 more rungs then your six above the middle but if you climb down 10 rungs then your 4 below the middle so if you climb back up 18 rungs and your at the very top then it took 4 rungs for you to climb back to the middle so subtract 4 from 18 and you get 14 and thats half of the rungs so multiply 14 by 2 whoe now you have 28 the answer wow thats sooo hard siiiike
stuh505 wrote:1) The ladder has a middle rung. That means there is an odd number of rungs. Let N be the number of rungs. We will use 1-based indexing.
2) He starts on the middle rung, M. That means
M = (N+1)/2
3) Starting from the middle rung, he climbs up 6, down 10, up 18, and this leaves him on the top rung.
M + 6 - 10 + 18 = N
Solve:
M = N - 14
N-14 = (N+1)/2
N+1 = 2N - 28
N = 2N - 29
N = 29
There are 29 rungs. He started on the 15th rung.
wrong he had to have stared on the 14 rung because theres only 28 rungs and half of 28 is 14 and also its illogical for him to start halfway if theres 29 rungs look ok
14 + 6 = 20 - 10 = 10 + 18 = 28 so Ha
Errr, bionic, if the fireman stood on the 14th rung on a 28 rung ladder as you say, how many rungs would be below him?
Answer = 13
How many rungs would he have above him?
Answer = 14
He is not, therefore, on the middle rung.
The correct answer must be 29 rungs, as only a ladder with an odd number of rungs can have a true middle rung.
the correct one is 28 because after the middle is 14 rungs
think about it we did not count the middle one to figure the half of the ladder why... for the same reason we are no suppose to count the step at flor level. so 14 is the exact half make two 14 rungs ladder in line and you will have 28 rungs (best is to draw this problem)
28 is the correct answer (sorry for my bad english)
AkinaThemis wrote:the correct one is 28 because after the middle is 14 rungs
think about it we did not count the middle one to figure the half of the ladder why... for the same reason we are no suppose to count the step at flor level. so 14 is the exact half make two 14 rungs ladder in line and you will have 28 rungs (best is to draw this problem)
28 is the correct answer (sorry for my bad english)
That is incorrect, I have already proven it.
The movement up from the middle rung was 14 (6-10+18) so the movement down must be 14 giving a total of 14 up plus 1 middle plus 14 down equals 29.
I like where doowop verbally bitch slapped bionic off his virtual ladder.
Stumble It!
Tweet This
Bookmark on Delicious
Share on Facebook
Share on MySpace