Practice problem

Systems of Linear Equations with No Solution - Definition & Practice

+3 contributors

Contributors

Taylor Evans
Victor Wang
Sarah Walker
Caroline K

Picture of an air traffic controller sitting at a desk with 2 computer monitors in front of him. He is wearing a headset to communicate with the active planes. — Image source: By erikvictor2005 CC0, via pixabay.com

Aircraft controllers monitor air traffic and make sure no crashes or collisions happen in the sky.

Suppose one plane is heading westward following the equation
$D = 600 - 10t$ . $D$ is the mile distance to the plane's destination (the city of Paris, Texas), and $t$ is the time that has passed, in minutes. Another plane is headed eastward for an around-the-world journey, with position $D = 8t-660$ relative to Paris, Texas.

For example, at time $t=0$ the first plane is $600$ miles east of Paris, Texas, while the second plane is $660$ miles west of Paris, Texas.

Suppose the two planes are flying at the same altitude at all times. Does the aircraft controller need to step in and prevent a collision? If your answer is yes, give a reason.