Q:

alec is climbing a 14 foot ladder where the rungs are 3/4 of a foot apart. there is one foot of space on each end of the ladder before the first and last rung. How many rungs are on the ladder that alec is climbing including the first and last one?

Accepted Solution

A:
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 =  [tex]\frac{3}{4}[/tex]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 feetThere 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 feetAs distance between each rung = [tex]\frac{3}{4}[/tex]Number of  [tex]\frac{3}{4}[/tex]  spaces in ladder of 12 feet =[tex]\frac{( 12)}{\frac{3}{4}}[/tex]Number of  [tex]\frac{3}{4}[/tex]  spaces in ladder of 12 feet=   [tex]\frac{(12\times4)}{3}[/tex]Number of  [tex]\frac{3}{4}[/tex]  spaces in ladder of 12 feet=[tex]\frac{(48)}{3}[/tex]Number of  [tex]\frac{3}{4}[/tex]  spaces in ladder of 12 feet =16And as for n spaces there will be n + 1 rungs, so for 16 spaces there will be 16 + 1 = 17 rungs.