Question

In one minute you climb halfway up a rock wall. And another minute you are 24 feet above the ground after covering half of the remaining height. Write an equation you can use to find the total height H of the Rockwall

Answer 1

Let H be the total height of rock wall.

We have been given that after one minute we climb half of the rock wall $\frac{H}{2}$ and after another minute we climb half of the remaining height that is $\frac{1}{2}\cdot \frac{H}{2}$.

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.

$\frac{H}{2}+\frac{1}{2}\cdot \frac{H}{2}=24\text{ feet}$

Now we will solve for H.

$\frac{H}{2}+ \frac{H}{4}=24\text{ feet}\\ \\ \frac{2H}{4}+\ \frac{H}{4}=24\text{ feet}\\ \\ \frac{3H}{4}=24\text{ feet}$

$H=\frac{24\cdot 4}{3}\\ \\ H=8\cdot 4=32$

Therefore, total height (H) of rock wall is 32 feet.

Answer 2

(1/2)H+(1/2)×(1/2)H=24
(1/2)H+(1/4)H=24
(3/4)H=24
H=32