Question

18 airplanes two airplanes leave the same airport heading in different directions. after 2 hours, one airplane has traveled 710 miles and the other has traveled 640 miles. describe the range of distances that represents how far apart the two airplanes can be at this time.

Explanation:

Step1: Consider the extreme cases

When two airplanes are moving in a straight - line, if they are moving in opposite directions (the maximum - distance case), the distance \(d\) between them is the sum of their distances. If they are moving in the same direction (the minimum - distance case, assuming one is faster), the distance \(d\) between them is the difference of their distances.
Let \(d_1 = 710\) miles and \(d_2=640\) miles.

Step2: Calculate the maximum distance

The maximum distance \(d_{max}\) occurs when the airplanes are moving in opposite directions. Using the formula \(d = d_1 + d_2\), we have \(d_{max}=710 + 640=1350\) miles.

Step3: Calculate the minimum distance

The minimum distance \(d_{min}\) occurs when the airplanes are moving in the same direction. Using the formula \(d=\vert d_1 - d_2\vert\), we have \(d_{min}=\vert710 - 640\vert = 70\) miles.

Answer:

The two airplanes are between \(70\) miles and \(1350\) miles apart. So the range of distances \(d\) is \(70\lt d\lt1350\)