SOLUTION: With a 50 mi/h tailwind, a plane flies 1200 miles in the same amount of time it can travel 1000 miles AGAINST a 50 mi/h headwind. What is the plane's speed in still air?

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Question 866727: With a 50 mi/h tailwind, a plane flies 1200 miles in the same amount of time it can travel 1000 miles AGAINST a 50 mi/h headwind. What is the plane's speed in still air?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Versus Wind__________Speed__________time_________distance
WITH_________________r+50____________t___________1200
AGAINST______________r-50____________t___________1000

r = speed of plane if wind absent
t = unknown time for both directions described

Uniform Motion Rate, RT=D for rate, time, distance.

Time WITH Wind:
t=1200%2F%28r%2B50%29

Time AGAINST Wind:
t=1000%2F%28r-50%29

The times were given as equal.
1200%2F%28r%2B50%29=1000%2F%28r-50%29
1200%28r-50%29=1000%28r%2B50%29
12%28r-50%29=10%28r%2B50%29
12r-600=10r%2B500
2r=500%2B600
r=1100%2F2
highlight%28r=550%29, plane's speed in still air.