Answer:
To solve this problem, we first need to find out how much time it will take for the airplane that is descending to reach the same altitude as the airplane that is ascending. To do this, we can use the formula d = r * t, where d is the distance, r is the rate, and t is the time.
In this case, the distance is the difference between the starting altitudes of the two airplanes, which is 42,000 feet for the descending airplane and 0 feet for the ascending airplane. The rate is the rate at which the descending airplane is descending, which is 3,500 feet per minute. Plugging these values into the formula, we get:
d = r * t
d = (3,500 feet/minute) * t
d = 42,000 feet
Solving for t, we get:
t = d / r
t = (42,000 feet) / (3,500 feet/minute)
t = 12 minutes
So it will take 12 minutes for the descending airplane to reach the same altitude as the ascending airplane.
To find the altitude at which the two airplanes will be at the same altitude, we can use the formula d = r * t, where d is the distance, r is the rate, and t is the time. In this case, the distance is the altitude at which the two airplanes will be at the same altitude, the rate is the rate at which the ascending airplane is ascending, which is 2,500 feet per minute, and the time is the time it will take for the descending airplane to reach the same altitude as the ascending airplane, which we calculated to be 12 minutes.
Plugging these values into the formula, we get:
d = r * t
d = (2,500 feet/minute) * (12 minutes)
d = 30,000 feet
Therefore, the altitude at which the two airplanes will be at the same altitude is 30,000 feet.
There are several other ways we could have solved this problem. For example, we could have used the formula d = r * t to find the altitude of the ascending airplane at the same time that the descending airplane reaches the same altitude, and then subtracted the starting altitude of the ascending airplane (0 feet) from this value to find the altitude at which the two airplanes will be at the same altitude.
Another way to solve this problem is to use the formula d = (v1 + v2) * t / 2, where d is the distance, v1 and v2 are the rates at which the two airplanes are moving, and t is the time. In this case, we can set d equal to the difference between the starting altitudes of the two airplanes, v1 equal to the rate at which the descending airplane is descending, v2 equal to the rate at which the ascending airplane is ascending, and t equal to the time it will take for the descending airplane to reach the same altitude as the ascending airplane.
Plugging these values into the formula, we get:
d = (v1 + v2) * t / 2
d = (3,500 feet/minute + 2,500 feet/minute) * (12 minutes) / 2
d = (6,000 feet/minute) * (12 minutes) / 2
d = (72,000 feet) / 2
d = 36,000 feet
Therefore, the altitude at which the two airplanes will be at the same altitude is 36,000 feet.
We can also solve this problem using a table to track the altitude of the two airplanes over time. We can start by making a table with