Final answer:
To find the altitude at which the two airplanes will be at the same height, divide the initial altitude difference by the rate of descent for the descending airplane and by the rate of ascent for the ascending airplane. Substitute the calculated time into either of the previous equations to solve for the remaining altitude variable.
Step-by-step explanation:
To find the altitude at which the two airplanes will be at the same height, we need to find the time it takes for each airplane to reach that altitude.
Let's start with the descending airplane. It is currently 39,900 feet above the ground and descending at a rate of 3,000 feet per minute. So, the time it takes for the descending airplane to reach the same altitude as the ascending airplane can be found by dividing the initial altitude difference by the rate of descent:
Time = Altitude Difference / Rate of Descent = (39,900 feet - Altitude of Ascending Airplane) / 3,000 feet per minute
Next, let's consider the ascending airplane. It is ascending at a rate of 2,700 feet per minute. So, the time it takes for the ascending airplane to reach the same altitude as the descending airplane can be found by dividing the initial altitude difference by the rate of ascent:
Time = Altitude Difference / Rate of Ascent = Altitude of Descending Airplane / 2,700 feet per minute
To find the altitude at which the two airplanes meet, we need to substitute the calculated time into either of the previous equations to solve for the remaining altitude variable.