SOLUTION: I need some help in trying to solve the following equation. I have been trying to solve it by using r+50 = 1200/t and r-50 = 1000/4-t but cant seem to get an answer that works back

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Question 143523: I need some help in trying to solve the following equation. I have been trying to solve it by using r+50 = 1200/t and r-50 = 1000/4-t but cant seem to get an answer that works back into the equation.
A jet traveling at a constant speed goes 1200km with the wind, then turns around and travels for 1000 km against the wint. If the speed of the wind is 50 km/h and the total flight took 4 hours, find the speed of the plane in still air.
Thank you.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A jet traveling at a constant speed goes 1200km with the wind, then turns around and travels for 1000 km against the wind. If the speed of the wind is 50 km/h and the total flight took 4 hours, find the speed of the plane in still air.
:
Try doing it this way, write a time equation, Time = dist%2Frate:
1200%2F%28%28r%2B50%29%29 + 1000%2F%28%28r-50%29%29 = 4
;
1200(r-50) + 1000(r+50) = 4(r-50)(r+50)
:
1200r - 60000 + 1000r + 50000 = 4(r^2 - 2500)
:
2200r - 10000 = 4r^2 - 10000
:
0 = 4r^2 - 2200r - 10000 + 10000
:
4r^2 - 2200r = 0
:
4r(r - 550) = 0
:
r = 550 km/hr speed in still air
:
:
Check solution by finding the times of each trip
1200/(550+50) = 2 hr
1000/(550-50) = 2 hr