Question

Keith is in a hot air balloon that is 200 feet above the ground and is descending 1.2 feet per second. Erica is in a hot air balloon that is 130 feet above the ground is ascending 0.4 feet per second. After how many seconds will the hot air balloons be the same number of feet above the ground?

A) 250 seconds
B) 300 seconds
C) 350 seconds
D) 400 seconds

Answer 1

By setting the height equations for both balloons equal to each other, we find that the balloons will be at the same altitude after 43.75 seconds, which is not listed in the provided choices.

Step-by-step explanation:

The question asks when the two hot air balloons, with one descending and one ascending, will be at the same number of feet above the ground. To solve this, we can set up an equation where the heights of the two balloons as functions of time are equal. Let's denote the time as t in seconds. For Keith's balloon, the equation will be 200 - 1.2t, and for Erica's balloon, it will be 130 + 0.4t. Setting these two equations equal gives us:

200 - 1.2t = 130 + 0.4t.

Now we solve for t:

1.6t = 70,

t = 70 / 1.6,

t = 43.75 seconds.

However, the answer choices provided do not include 43.75 seconds, indicating there might be a misunderstanding or a typo in the options. If the student is looking for an answer among the given choices, none of them are correct.