Answer
$401.5$ inches
(33.46 ft)
Work Step by Step
The rung length in inches forms an arithmetic sequence, with
$a_{1}=49, d=-2.5,$ and $a_{n}=24$
The nth term is $a_{n}=a_{1}+(n-1)d$
$\quad 24=49+(n-1)(-2.5)\qquad$ ... solve for n
$-25=-2.5(n-1)$
$10=n-1$
$11=n$
There are 11 rungs.
$S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$
The sum of 11 rung lenths is
$S_{11}=\displaystyle \frac{11}{2}(49+24)=401.5$ inches
(33.46 ft)