Question

Two hot air balloons are traveling along the same path away from a town, beginning from different locations at the same time. Henry’s balloon begins 30 miles from the town and is 48 miles from the town after 2 hours. The distance of Tasha’s balloon from the town is represented by the function y = 8x + 20. Which balloon was farther from the town at the beginning, and which traveled more quickly? A. Tasha’s balloon was farther from the town at the beginning, and it traveled more quickly. B. Tasha’s balloon was farther from the town at the beginning, but Henry’s balloon traveled more quickly. C. Henry’s balloon was farther from the town at the beginning, and it traveled more quickly. D. Henry’s balloon was farther from the town at the beginning, but Tasha’s balloon traveled more quickly.

Answer 1

Henry's balloon was farther from the town at the beginning, starting at 30 miles away. Tasha's balloon started closer at 20 miles from town. Henry's balloon traveled at 9 miles per hour, while Tasha's balloon traveled at 8 miles per hour, making Henry's balloon the faster one. Therefore, the correct option is D.

Step-by-step explanation:

To determine which hot air balloon was farther from the town at the beginning and which traveled more quickly, let's analyze the information provided.

Henry's balloon was 30 miles from the town at the start and 48 miles away after 2 hours. Therefore, Henry's balloon traveled 18 miles in 2 hours, which is 9 miles per hour.

Tasha's balloon's distance from the town is given by the function y = 8x + 20.

If we assume the variable x represents the number of hours, then after 2 hours, Tasha's balloon would be

y = 8(2) + 20 = 36 miles away from the town.

Tasha started 20 miles away from the town and after 2 hours is 36 miles away, which indicates she traveled 16 miles in 2 hours, making her speed 8 miles per hour.

Therefore, the correct answer is: Henry's balloon was farther from the town at the beginning, but Tasha's balloon traveled more quickly.