At 5:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 17580 ft. and is descending at the rate of 310 ft/min. Airplane #2 has an elevation of 12700 ft. and is descending at the rate of 500 ft/min.

At 5:20 am, Airplane #2 quickly levels off its flight and flies horizontally. At 5:55 am, this plane then begins to climb at 200 ft/min.

(1) Let t\displaystyle {t} represent the time in minutes since 5:00 am, and let E\displaystyle {E} represent the elevation in feet. Write an equation for the elevation of each plane in terms of t\displaystyle {t}. Note that the equation for plane #2 will have 3 separate pieces.

plane #1: E(t)=\displaystyle {E}{\left({t}\right)}=  
plane #2 (descent): E(t)=\displaystyle {E}{\left({t}\right)}=  
plane #2 (steady elevation): E(t)=\displaystyle {E}{\left({t}\right)}=  
plane #2 (ascent): E(t)=\displaystyle {E}{\left({t}\right)}=  

(2) At what time will the two airplanes have the same elevation?
t=\displaystyle {t}= minutes after 5:00 am  

(3) What is the elevation at that time?
E=\displaystyle {E}= feet