SOLUTION: Having trouble setting up the equation for word problem: At 6:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 10140 ft. and climbs 1500 feet every 5

Question 1072503: Having trouble setting up the equation for word problem: At 6:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 10140 ft. and climbs 1500 feet every 5 minutes. Airplane #2 has an elevation of 4340 ft. and climbs 1500 feet every 3 minutes.
(1)Let t represent the time in minutes since 6:00 am, and let E represent the elevation in feet. Write the equations for the elevations of each plane in terms of t plane #1:
E(t)=
E(t)=
plane #2:
E(t)=
E(t)=
(2)At what time will the two airplanes have the same elevation?
t=
t= minutes after 6:00 am Preview
(3) What is the elevation at that time?
E=
E= feet
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Airplane #1 has an elevation of 10140 ft. and climbs 1500 feet every 5 minutes. Airplane #2 has an elevation of 4340 ft. and climbs 1500 feet every 3 minutes.
(1)Let t represent the time in minutes since 6:00 am, and let E represent the elevation in feet.
Write the equations for the elevations of each plane in terms of t
plane #1:
I'm not sure I know what they want here, it's a simple problem, just write an equation for each plane.
Find the climbing rate of each plane
1500/5 = 300 ft/min
and
1500/3 = 500 ft/min
then
Plane 1: E(t) = 300t + 10140
Plane 2: E(t) = 500t + 4340
Find the time for them to be at the same altitude
500t + 4340 = 300t + 10140
500t - 300t = 10140 - 4340
200t = 5700
t = 5800/200
t = 29 minutes so the time would be 6:29
:
Find the altitude at this time using the first plane equation
E(t) = 300(29) + 10140
E(t) = 8700 + 10140
E(t) = 18840 ft, plane #1
:
Check this in the 2nd equation
E(t) = 500(29) + 4340
E(t) = 14500 = 4340
E(t) = 18840 ft, plane #2
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