Sure! Let's analyze the problem step-by-step:
1. Initial Distances:
- Henry's balloon starts at a distance of 25 miles from the town.
- The initial equation for Tasha's balloon is [tex]\( y = 7x + 15 \)[/tex], where [tex]\( x \)[/tex] represents time in hours and [tex]\( y \)[/tex] represents the distance from the town. When [tex]\( x = 0 \)[/tex] (at the starting point), the distance [tex]\( y \)[/tex] for Tasha's balloon is [tex]\( y = 7(0) + 15 = 15 \)[/tex] miles.
Conclusion: Henry's balloon was farther from the town at the beginning.
2. Calculating Speeds:
- For Henry's balloon: After 2 hours, his distance from the town is 37 miles. His initial distance was 25 miles. Thus, the distance traveled in 2 hours = [tex]\( 37 - 25 = 12 \)[/tex] miles. Therefore, Henry's speed = [tex]\( \frac{12 \text{ miles}}{2 \text{ hours}} = 6 \text{ miles per hour} \)[/tex].
- For Tasha's balloon: The distance formula given is [tex]\( y = 7x + 15 \)[/tex]. This indicates Tasha's speed is the coefficient of [tex]\( x \)[/tex], which is 7 miles per hour.
Conclusion: Tasha's balloon traveled more quickly.
3. Decision Making:
Based on our analysis:
- Henry's balloon was farther from the town at the beginning (25 miles vs. 15 miles).
- Tasha's balloon traveled more quickly (7 miles per hour vs. 6 miles per hour).
Hence, the correct answer is:
A. Henry's balloon was farther from the town at the beginning, but Tasha's balloon traveled more quickly.
