i need help on this question quick!!

Question

It takes a bird 6 minutes to fly with a 10 mph tailwind from its nest to a bird feeder. It takes 30 minutes for the bird to get back to its nest. What is the bird’s speed in still conditions? How far away is the bird feeder?

Answer 1

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.

Let:

r= speed of the bird in still condition.

r + 10 = speed of the bird from the nest with the tailwind to the feeder

t_f=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

t_b=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)