Question 938308
"A bird takes 45 min to make a 480 m round trip between two trees.  Flying 0.25 m against the wind on the first half takes the same time as flying 0.5 m with the wind on the return flight.  Find the rate of the bird in calm conditions and the rate of the wind."
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It's flying 2x as fast downwind as upwind (its groundspeed)
Call r its upwind groundspeed --> 2r downwind.
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The round trip avg speed = 2*r*2r/(r + 2r) = 4r/3
The round trip avg speed = d/t = 480/(3/4) = 640 m/hr
4r/3 = 640
r = 480 m/hr upwind
downwind speed = 2r = 960 m/hr
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The bird's airspeed is the average of upwind & downwind groundspeeds
= 720 m/hr
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windspeed is the difference between airspeed & groundspeed = 240 m/hr