An airplane is preparing to land at an airport. It is 52,200 feet above the ground and is descending at the rate of 3,100 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.

Part A:

9 Minutes

Part B:

The first method by direct calculation is faster

Step-by-step explanation:

Part A:

The height of the first airplane = 52,200 feet

The rate of descending of the first airplane = 3,100 feet per minute

The rate of ascent of the second airplane from the ground = 2,700 feet per minute

Therefor, we have;

3100 × t = x

2700× t = 52200 - x

∴ 2700× t = 52200 - 3100 × t

5800 × t = 52200

t = 52200/5800 = 9 minutes

Therefore, the time both planes will be  at the same height = 9 minutes

Part B:

1) Another method is to determine how long it will take the first plane to land and the second plane to ascend to 52200 feet, then find the ratio of the duration and estimate what time both plane will cover a distance of 52200 feet

2) A third method is to plot the graph of motion and find the point of intersection of the equation of motion of both airplanes

The first method by direct calculation is faster

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step-by-step explanation: