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

Question 186854: 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 of the airplane.

can you solve this for me?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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
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