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.
Whích balloon was farther from the town at the beginning, and which traveled
more quickly?
O
A. Tasha's balloon was farther from the town at the beginning, but
Henry's balloon traveled more quickly.
O
B. Tasha's balloon was farther from the town at the beginning, and it
traveled more quickly.
O
C. Henry's balloon was farther from the town at the beginning, but
Tasha's balloon traveled more quickly.
O
D. Henry's balloon was farther from the town at the beginning, and it
traveled more quickly.​

Answer 1

Tasha's balloon was farther from the town at the beginning, and Henry's balloon traveled more quickly.

Step-by-step explanation:

To determine which balloon was farther from the town at the beginning, we can compare the distances of Henry's and Tasha's balloons from the town. Henry's balloon began 30 miles from the town, while Tasha's balloon is represented by the function y = 8x + 20. Since Tasha's balloon is at a positive distance from the town (y > 0) when x = 0, we can conclude that Tasha's balloon was farther from the town at the beginning.

To determine which balloon traveled more quickly, we can compare their rates of change. Tasha's balloon has a rate of change of 8, meaning that for every hour that passes (x increases by 1), Tasha's balloon moves 8 miles away from the town. Henry's balloon traveled from 30 miles to 48 miles in 2 hours, which corresponds to a rate of change of (48-30)/2 = 9 miles per hour. Therefore, Henry's balloon traveled more quickly than Tasha's balloon.

Answer 2

Henry's balloon was farther from the town at the beginning and Henry's balloon traveled more quickly.

Step-by-step explanation:

The distance of Tasha's balloon from the town is represented by the function y = 8x+ 20 ............. (1)

Where y is the distance in miles from the town and x represents the time of fly in hours.

So, at the start of the journey i.e. at x = 0, y = 20 miles {From equation (1)} from the town.

Again, Tasha's balloon is traveling at a rate of 8 miles per hour.

Now, Henry's balloon begins 30 miles from the town and is 48 miles from the town after 2 hours.

So, Henry's balloon traveling with the speed of miles per hour.

Therefore, Henry's balloon was farther from the town at the beginning i.e. 30 miles from the town. And Henry's balloon traveled more quickly i.e at the rate of 9 miles per hour. (Answer)