Answer:
350 mph
Step-by-step explanation:
You want the speed of a plane in still air if a trip of 600 miles with a 50 mph wind is 1/2 hour shorter than the same trip against the wind.
Time
The relation between time, speed, and distance is ...
t = d/s
If p is the speed of the plane, then its speed with the wind is (p+50) and its speed against the wind is (p-50).
The difference in times for the two trips is ...
600/(p-50) -600/(p+50) = 1/2
Solution
600(1/(p-50)-1/(p+50)) = 1/2
((p+50)-(p-50))/((p-50)(p+50)) = 1/1200 . . . . . divide by 600
p² -50² = 120000 . . . . combine fractions, invert both sides
p = √122500 = 350
The speed of the plane in still air is 350 mph.
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Additional comment
The trip to Oakland takes 1 1/2 hours; the return takes 2 hours.
