Calculate the total distance in miles the bird travels?

Question

The distance between Station Atena and Station Barcena is 90 miles. A train starts from Atena towards Barcena. A bird starts at the same time from Barcena straight towards the moving train. On reaching the train, it instantaneously turns back and returns to Barcena. The bird makes these journeys from Barcena to the train and back to Barcena continuously till the train reaches Barcena. The bird finally returns to Barcena and rests. Calculate the total distance in miles the bird travels in the following two cases:
(a) The bird flies at 90 miles per hour and the speed of the train is 60 miles per hour.
(b) the bird flies at 60 miles per hour and the speed of the train is 90 miles per hour

Answer 1

a) 135 miles
It takes the train 1.5 hrs to reach Barcena, so the bird flies 1.5 hrs at 90 mph = 135 miles.

b) 60miles
It takes the train 1 hr to reach Barcena so the bird flies for an hour at 60mph. So it flies 60 miles

Answer 2

a) Time taken by the train to reach Barcena= 90/60 hours = 90 minutes.
As spped of bird is more, it will continue flying back and forth for 90 minutes with 90 miles per hour.
So Total distance the bird travels= 90* 90/60= 135 miles.

b) They will meet at time t given by:
60t + 90 t= 90
t=9/15 hours = 36 minutes.
As the spped of train is more, it will reach Bercena first. So the bird aftet meeting the train at a distance of 36 miles( 60* 36/60) will simply get back.
So total distance= 36*2= 72 miles.

Answer 3

135miles is a wrong answer, because bird flies faste in 1st case so the bird takes some less amount of time to reach train and back to station.time taken by both the train and bird or not equal. they havent given that both train and bird has reached at the same time. A guy below given a calculation fj123456 is correct

Answer 4

let t be the time after the train start,
let a be the speed of train,
let b be the speed of bird.

At time t, the train will be (t*a) mile from Atena, ie, (90-t*a) miles from Barcena.

For the bird to reach the train, 90-t*a=t*b
a)

a=60, b=90
90-60t=90t
90=150t
t=0.6 hours
distance for bird travel=2*0.6*90=108miles

b)

a=90, b=60
90-90t=60t
90=150t
t=0.6 hours
distance for bird travel=2*0.6*90=108miles

Answer 5

How long does it take the train to reach Barcena, and how far can the bird fly in that interval?

a) 1.5 hours; 135 miles
b) 1 hour; 60 miles

Answer 6

Is the bird an African or European Swallow?

Answer 7

a) 145
b) 72