Question

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3094 feet and Plane B is just taking off. Plane A is gaining altitude at 20.25 feet per second and Plane B is gaining altitude at 75.5 feet per second.

How many seconds will pass before the planes are at the same altitude?

What will their altitude be when theyre at the same altitude?

Answer 1

Sorry idk this but at least I said hi

Answer 2

so, plane A is at 3094 and gaining altitude at 20.25 fps, thus every passing second "s", it gains that much.  Now, it starts at 3094, and thus the 20.25 is adding up to it, therefore, after 1s is at 3094 + 20.25(1), after 2s is at 3094 + 20.25(2), after 3s is at 3094 + 20.25(3), after "s" seconds is at 3094 + 20.25(s) or 3094 + 20.25s.

likewise, the plane B is just taking off, so it has altitude of 0, and gaining at 75.5 per second, so, after 1s is at 0 + 75.5(1), after 2s is at 0 + 75.5(2), after 3s is at 0 + 75.5(3) and after "s" seconds is at 0 + 75.5(2) or 75.5s.


when both are the same altitude, it means their altitude is the same, and how long is that anyway?

$\bf \stackrel{\textit{plane A}}{3094+20.25s}=\stackrel{\textit{plane B}}{75.5s}\implies 3094=75.5-20.25\\\\\\ 3094=55.25s\implies \cfrac{3094}{55.25}=s\implies 56=s$

what's their altitude at that time anyway?   $\bf \begin{cases} \stackrel{\textit{plane A}}{3094+20.25(56)}\\\\ \stackrel{\textit{plane B}}{75.5(56)} \end{cases}$