5. A hot air balloon is at an altitude of \( 100 \frac{1}{5} \) yards. The balloon's altitude decreases by \( 10 \frac{4}{5} \) yards every minute. Determine the number of minutes it will take the balloon to reach an altitude of 57 yards. (Example 2)

To determine how many minutes it will take for the hot air balloon to descend from an altitude of \( 100 \frac{1}{5} \) yards to 57 yards, follow these steps: ### 1. Convert Mixed Numbers to Improper Fractions or Decimals It's easier to work with either improper fractions or decimals. We'll use decimals for simplicity. - **Initial Altitude:** \[ 100 \frac{1}{5} = 100 + 0.2 = 100.2 \text{ yards} \] - **Rate of Descent:** \[ 10 \frac{4}{5} = 10 + 0.8 = 10.8 \text{ yards per minute} \] ### 2. Set Up the Equation Let \( t \) be the number of minutes it takes to reach 57 yards. The altitude decreases linearly, so: \[ \text{Final Altitude} = \text{Initial Altitude} - (\text{Rate of Descent} \times t) \] Plugging in the known values: \[ 57 = 100.2 - 10.8t \] ### 3. Solve for \( t \) First, isolate the term with \( t \): \[ 100.2 - 57 = 10.8t \] \[ 43.2 = 10.8t \] Now, solve for \( t \): \[ t = \frac{43.2}{10.8} = 4 \] ### 4. Conclusion It will take **4 minutes** for the hot air balloon to descend from \( 100 \frac{1}{5} \) yards to 57 yards. **Answer:** 4 minutes