From the start, the bird is flying with the same direction as the tailwind. But from the feeder going back home, the bird is against the wind.
Formula is d=rt
where: d= distance, r=rate and t=time.
r= speed of the bird in still condition.
r + 10 = speed of the bird from the nest with the tailwind to the feeder
tf=6 mins. = 1/10 hr.= time from start to the feeder.
(r+10)(1/10) = distance from the nest to feeder.
r-10=speed of the bird from the feeder against the wind back to the nest
tb=30 min. =1/2 hr. =time from the feeder to nest
(r-10)(1/2) = distance from feeder to nest.
The distance from nest to feeder is the same as the distance from feeder to nest.
(r+10)(1/10) = (r-10)(1/2)
multiply 10 both sides:
r+10 = 5(r-10)
r+10 = 5r-50
r-5r = -10-50
-4r = -60
r=15 mph (the speed of the bird in still condition)
d = (15+10)(1/10) =25/10
d = 2.5 miles (the distance from nest to feeder)