Henry and Wayne operate a charter flying service out of Breckenridge, which has an elevation of 9,600 feet above sea level.

Question

Henry has two flights scheduled for the day. He is taking a couple from Breckenridge to Hamilton which has a drop of 35% in elevation. At Hamilton, he is picking up 3 business men and taking them to Denver which has a drop in elevation of 15% from Hamilton. This puts them at an elevation of
feet above sea level.

Wayne also has two flights scheduled for the day. He is taking a family from Breckenridge to Colorado Springs which has a -drop in elevation. At Colorado Springs, he is picking up some fishermen and taking them to Englewood which has a -drop in elevation from Colorado Springs. This puts them at an elevation of
feet above sea level.

After Henry and Wayne have both finished their two flights of the day, the final difference in their elevations from each other is
feet.

Answer 1

To calculate the elevations for Henry and Wayne's flights, we need to perform the required percentage drops step by step.

Henry's Flights:

1. From Breckenridge to Hamilton:

   • Initial elevation of Breckenridge: 9,600 feet
   • Drop in elevation: 35%
   • The drop in feet can be calculated as follows: \[ \text{Drop} = 9,600 \text{ feet} \times 0.35 = 3,360 \text{ feet} \]
   • The elevation at Hamilton: \[ 9,600 \text{ feet} - 3,360 \text{ feet} = 6,240 \text{ feet} \]

2. From Hamilton to Denver:

   • Drop in elevation from Hamilton: 15%
   • The drop in feet from Hamilton: \[ \text{Drop} = 6,240 \text{ feet} \times 0.15 = 936 \text{ feet} \]
   • The elevation at Denver: \[ 6,240 \text{ feet} - 936 \text{ feet} = 5,304 \text{ feet} \]

So Henry finishes at an elevation of 5,304 feet.

Wayne's Flights:

1. From Breckenridge to Colorado Springs:

   • Assuming Colorado Springs has the same drop percentage as Hamilton, 35%. (If this is incorrect, please specify the drop for Colorado Springs and Englewood.)
   • Drop in elevation to Colorado Springs: \[ \text{Drop} = 9,600 \text{ feet} \times 0.35 = 3,360 \text{ feet} \]
   • The elevation at Colorado Springs: \[ 9,600 \text{ feet} - 3,360 \text{ feet} = 6,240 \text{ feet} \]

2. From Colorado Springs to Englewood:

   • Assuming a similar drop of 15% for Wayne's second flight (like Denver).
   • Drop in elevation from Colorado Springs: \[ \text{Drop} = 6,240 \text{ feet} \times 0.15 = 936 \text{ feet} \]
   • The elevation at Englewood: \[ 6,240 \text{ feet} - 936 \text{ feet} = 5,304 \text{ feet} \]

So Wayne finishes at an elevation of 5,304 feet.

Final Difference in Elevations:

• Henry's elevation: 5,304 feet
• Wayne's elevation: 5,304 feet
• Difference: \[ |5,304 - 5,304| = 0 \text{ feet} \]

Final Summary:

• Henry's final elevation: 5,304 feet
• Wayne's final elevation: 5,304 feet
• Difference in elevations: 0 feet