Answer:
Alec is climbing 17 rungs on the ladder of 14 feet ( including first and last rung ) .
Step-by-step explanation:
Given:
Length of the ladder = 14 foot
Distance between Rungs in ladder = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
There is one foot of space on each end of the ladder before the first and last rung .
To Find:
Number of rungs are on the ladder =?
Solution:
Let us assume there are 3 rungs. Between 3 rungs there will be two spaces. between four rungs there will be 3 spaces , so between n + 1 rungs there will be n spaces.
Given that length of the ladder = 14 feet
There is one foot of space on each end before the first and last rung.
So length of the ladder between first and last rung = 14 – 2 ( 1 foot of each side) = 12 feet
As distance between each rung = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
Number of
spaces in ladder of 12 feet =![\frac{( 12)}{\frac{3}{4}}](https://tex.z-dn.net/?f=%5Cfrac%7B%28%2012%29%7D%7B%5Cfrac%7B3%7D%7B4%7D%7D)
Number of
spaces in ladder of 12 feet= ![\frac{(12\times4)}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%2812%5Ctimes4%29%7D%7B3%7D)
Number of
spaces in ladder of 12 feet=![\frac{(48)}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%2848%29%7D%7B3%7D)
Number of
spaces in ladder of 12 feet =16
And as for n spaces there will be n + 1 rungs, so for 16 spaces there will be 16 + 1 = 17 rungs.