Question

A hot-air balloon 70 meters above the ground is falling at a constant rate of 6

meters per second while another hot-air balloon 10 meters above the ground is
rising at a constant rate of 15 meters per second. To the nearest tenth of a second,
after how many seconds will the 2 balloons be the same height above the
ground?
A. 8.9
B. 6.7
C. 2.9
D. 0.4
E. 0.2

Answer 1

The answer is C: 2.9 seconds.

Explanation:

To solve this problem, you can set up an equation representing the distance each balloon travels over time, and then solve for the time at which they will be at the same height.

The equation for the first balloon is:

70 - 6t = h (h is the height of the first balloon at time t)

The equation for the second balloon is:

10 + 15t = h (h is the height of the second balloon at time t)

If we set the two equations equal to each other and solve for t, we get:

70 - 6t = 10 + 15t

16t = 60

t = 60/16 = 3.75 seconds

The two balloons will be at the same height after approximately 3.75 seconds. Therefore, the answer is C: 2.9 seconds.