Let H be the total height of rock wall.
We have been given that after one minute we climb half of the rock wall [tex]\frac{H}{2}[/tex] and after another minute we climb half of the remaining height that is [tex]\frac{1}{2}\cdot \frac{H}{2}[/tex].
We are also given that after two minutes we are 24 feet above ground. To figure out total height (H) of the rock wall we will substitute our given information in an equation.
[tex]\frac{H}{2}+\frac{1}{2}\cdot \frac{H}{2}=24\text{ feet}\\[/tex]
Now we will solve for H.
[tex]\frac{H}{2}+ \frac{H}{4}=24\text{ feet}\\ \\ \frac{2H}{4}+\ \frac{H}{4}=24\text{ feet}\\ \\ \frac{3H}{4}=24\text{ feet}[/tex]
[tex]H=\frac{24\cdot 4}{3}\\ \\ H=8\cdot 4=32[/tex]
Therefore, total height (H) of rock wall is 32 feet.
