College

A helium balloon was released from a height of 0 feet and rose [tex]97 \frac{1}{2}[/tex] feet in 10 minutes. It then descended [tex]97 \frac{1}{2}[/tex] feet in the next 45 minutes. What was the balloon's final height?

A. 0 feet
B. [tex]48 \frac{3}{4}[/tex] feet
C. [tex]97 \frac{1}{2}[/tex] feet
D. 195 feet

Answer :

To solve the problem, let's break it down step by step.

1. Initial Position: The helium balloon starts at a height of 0 feet.

2. Balloon Rises: The balloon ascends 97 1/2 feet, which can be expressed as 97.5 feet. So, starting from 0 feet and rising 97.5 feet, the balloon reaches a height of:
[tex]\[
0 + 97.5 = 97.5 \text{ feet}
\][/tex]

3. Balloon Descends: After reaching 97.5 feet, the balloon then descends 97 1/2 feet, which is also 97.5 feet. So, from the height of 97.5 feet, it descends back to:
[tex]\[
97.5 - 97.5 = 0 \text{ feet}
\][/tex]

4. Final Height: After these movements, the final height of the balloon is 0 feet.

Given the calculations, the balloon's final height is 0 feet. Thus, the correct answer is:

A. 0 feet