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

Answer:the bird flies at 60 miles per hour and the speed of the train is 90 miles per hour

The train (at a speed of 60 miles per hour) travels 60 miles in 60 minutes.

Therefore, the train travels from Atena to Barcena (84 miles) in 84 minutes.

Importantly, the bird makes the journeys continuously back and forth for this same amount of time (namely, 84 minutes).

Thus, the total distance traveled by the bird

= 80 miles per hour × 84 minutes = 80 × 84 / 60 miles = 112 miles.

Case 2: Bird flies at a speed less than that of the train

In 36 minutes, the bird travels 36 miles, the train travels 48 miles, and the two meet.

Now, the train (which is traveling at a speed greater than that of the bird) will reach Barcena before the bird.

So, the bird simply returns to Barcena (a return journey of 36 miles).

Thus, the total distance traveled by the bird is 72 miles.

Answer 2

Answer:

(a) The bird flies a total of 112 miles during its journey.

(b)The bird flies a total of 72 miles during its journey.

Step-by-step explanation:

Given Data:

There are 90 miles between Station Atena and Station Barcena.

To Find:

The total number of miles the bird travels in each case.

Calculation:

(i) The train travels at 90 miles per hour while the bird flies at 60 miles per hour.

The train covers 60 miles in 60 minutes at a speed of 60 mph.

As a result, the 84 kilometers between Atena and Barcena are covered by the train in 84 minutes.

It's significant that the bird makes the same number of back and forward trips continually (namely, 84 minutes).

Thus, the total distance traveled by the bird

= 80 miles per hour × 84 minutes = $80 \times \frac{84}{60}$ miles = 112 miles.

The bird covered a total distance of 112 miles by traveling at a speed of 80 miles per hour for 84 minutes.

Case 2: The speed of the bird is slower than that of the train.

The train travels 48 miles, the bird travels 36 miles, and they meet after 36 minutes.

The train will now arrive in Barcena before the bird since it is moving faster than the bird.

The bird simply returns to Barcena as a result (a return journey of 36 miles).

Thus, The bird has covered a total of 72 miles distance.

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