Question

An airplane is preparing to land at an airport. It is 50400 feet above the ground and is descending at the rate of 3000 feet per minute. At the same​ airport, another airplane is taking off and will ascend at the rate of 2600 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.

Answer 1

The two airplanes will be at the same altitude after 9 minutes, at 23400 feet above the ground.

Step-by-step explanation:

To find when the two airplanes will be at the same altitude and what that altitude will be, we can set up a system of equations. Let t be the time in minutes since the airplanes started their respective movements. The equation for the descending airplane is: 50400 - 3000t = altitude. The equation for the ascending airplane is: 2600t = altitude. To find when the altitudes are equal, we can set the two equations equal to each other and solve for t. By substituting this value of t into either equation, we can find the altitude at that time.

Method 1:

1. 50400 - 3000t = 2600t
2. 5600t = 50400
3. t = 9 minutes
4. Substituting t=9 into 50400 - 3000t:
5. 50400 - 3000(9) = altitude
6. 50400 - 27000 = altitude
7. 23400 = altitude

So, after 9 minutes, the two airplanes will be at the same altitude, which is 23400 feet above the ground.

Method 2:

Alternatively, we can graph the two equations and find the point of intersection. Plotting the two equations on a graph, we can see that the point of intersection corresponds to t=9 and altitude=23400. This confirms our previous result.

Method 1, setting up and solving the equations, is easier to use because it requires less visualization and can be done algebraically. Method 2, graphing the equations, is more difficult to use because it requires graphing and visually identifying the intersection point.

Answer 2

let t = no of minutes when they are at the same altitude

:

52200 - 3300t = 2500t

52200 = 3300t + 2500t

52200 = 5800t

t = 52200/5800

t = 9 minutes they will be at the same altitude

:

The altitude:

9*2500 = 22500 ft

:

Check on other train

52200 - 9(3300) =

52200 - 29700 = 22500 ft