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An airplane is preparing to land at an airport. It is 41,300 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 2,800 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.

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sqdancefan

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Answer:

  • after 7 minutes
  • 19,600 feet

Step-by-step explanation:

Here's the "pencil and paper" solution:

  The two altitude equations are ...

  • y = 41300 -3100x
  • y = 2800x

They can be solved by setting the expressions for y equal to each other.

  2800x = 41300 -3100x

  5900x = 41300

  x = 41300/5900 = 7

  y = 2800·7 = 19600

The planes will both be at 19,600 feet after 7 minutes.

_____

Attached are solutions from a graphing calculator, and from a calculator app that is able to solve systems of equations.

I find the graphing calculator the easiest to use. I can enter equations using a keyboard, and the solution is displayed in a form that can be copied and pasted.

The calculator app on my phone requires equation entry using a small on-screen keyboard, with multiple key hits required to access some functions. (y is obtained by hitting the x key twice, for example.)

The "pencil and paper" solution is not so difficult, but requires a certain amount of writing (or good short-term memory). The solutions for x and y require separate calculations, whereas the other methods give both x and y at the same time.

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