Question

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during the annual hot air balloon rally, hot air balloon pilots track their altitude as they travel. during a flight that began at 981 meters above sea level, one pilot tracked and recorded her altitude every half hour.
time (hr) | altitude change (m)
--- | ---
$\frac{1}{2}$ | 226.86
1 | $-66\frac{4}{8}$
$1\frac{1}{2}$ | -15.32
2 | $172\frac{3}{4}$
what is her altitude, in meters, after two hours?

Explanation:

Step1: Identify all altitude changes

We have altitude changes at \( \frac{1}{2} \) hr: \( 226.86 \) m, at 1 hr: \( -66\frac{4}{8} = -66.5 \) m, at \( 1\frac{1}{2} \) hr: \( -15.32 \) m, and at 2 hr: \( 172\frac{3}{4} = 172.75 \) m.

Step2: Sum the altitude changes

To find the total altitude after 2 hours, we sum all these changes:
\( 226.86 + (-66.5) + (-15.32) + 172.75 \)

First, calculate \( 226.86 - 66.5 = 160.36 \)
Then, \( 160.36 - 15.32 = 145.04 \)
Finally, \( 145.04 + 172.75 = 317.79 \)

Answer:

317.79