Question

GUYS PLEASE HELP ASAAAAP

Two hot air baloons are traveling along the same path away from a town, beginning from different locations at the same time. Henry’s balloon begins 10 miles from the town and is 24 miles from the town after 2 hours. The distance of Tasha’s balloon from the town is represented by the function y = 6x + 15.

Which balloon was farther from the town at the beginning, and which traveled more quickly?

A.
Henry’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, but Tasha’s balloon traveled more quickly.
D.
Tasha’s balloon was farther from the town at the beginning, and it traveled more quickly.

Answer 1

B. Tasha’s balloon was farther from the town at the beginning, but Henry’s balloon traveled more quickly.

Explanation:

To answer this question, we will look at the equation and numbers given and figure out details about these two balloons. Looking at the answer options, we need the distance from the town and the rate or speed ("how fast" they were traveling) of both balloons.

Rate:

We will find the rate of Henry's balloon. To do this, we can divide distance by time.

(24 miles - 10 miles) / 2 hours = 7 mph

Tasha's rate is given to us in the equation, it's 6 mph ("y = 6x + 15").

Distance:

It's given that Henry is 10 miles from the town.

In the equation given for Tasha's balloon, we see that she is 15 miles away from the town ("y = 6x + 15").

Conclusion:

In summary, Henry is traveling faster and Tasha starts farther away.

Looking at the answer options leads us to select answer B as the correct answer.

B. Tasha’s balloon was farther from the town at the beginning, but Henry’s balloon traveled more quickly.