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 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. Tasha's balloon was farther from the town at the beginning, but Henry's balloon traveled more quickly.
B. Tasha's balloon was farther from the town at the beginning, and it 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.
Thanks! :D
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, but Henry's balloon traveled more quickly.
B. Tasha's balloon was farther from the town at the beginning, and it 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.
Thanks! :D
Answers & Comments
Step-by-step explanation:
After 2 hours, Henry's balloon is 24 miles from the town, which means it has traveled 24 - 10 = 14 miles away from its starting point. We can find the speed of Henry's balloon by dividing the distance traveled by the time taken: 14 miles / 2 hours = 7 miles per hour.
Tasha's balloon is represented by the function y = 6x + 15, where x is the time in hours. After 2 hours, Tasha's balloon is at a distance of y = 6(2) + 15 = 27 miles from the town. This means Tasha's balloon was farther from the town at the beginning, since the y-intercept of the function is 15, which is greater than the starting distance of Henry's balloon.
To find the speed of Tasha's balloon, we can look at the coefficient of x in the function, which is 6. This means that Tasha's balloon is traveling at a speed of 6 miles per hour.
Therefore, the answer is:
A. Tasha's balloon was farther from the town at the beginning, but Henry's balloon traveled more quickly.
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Answer:
D. Henry's started farther, went faster
Step-by-step explanation:
Henry's balloon traveled 18 additional miles (from 30 to 48) in 2 hours, so had a speed of 18mi/(2h) = 9 mi/h. The equation for his position could be ...
y = 9x +30 . . . . . 9 is the rate of change; 30 is the initial value
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Comparing this to Tasha's position function, we see her balloon started 20 miles from town and traveled 8 miles per hour.
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Henry started farther from town and traveled faster.