SOLUTION: A plane takes 6 hours to fly from San Francisco to New York, and 5 hours to return back. The wind velocity is 50 miles per hour, from New York to San Francisco. What is the speed o

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Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate (speed) or the plane in still air
Then r+50=rate of plan with the wind (return trip)
And r-50=rate of plane against the wind (SF to NY)

time to fly to NY:
6=d/(r-50)-----------------eq1
time to return:
5=d/(r+50)-----------------eq2
from eq1, d=6(r-50). Substitute this into eq2 for d
5=6(r-50)/(r+50) multiply each side by (r+50)
5(r+50)=6(r-50) get rid of parens
5r+250=6r-300 add 300 to and subtract 5r from both sides
250+300+5r-5r=6r-5r-300+300 collect like terms
r=550 mph---------------------speed of plane in still air
CK
distance to SF=(550-50)*6=3000 mi
return distance=(550+50)*5=3000 mi
3000=3000
Hope this helps---ptaylor