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Math Puzzles & Brain Teasers

The Bird and the Train

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 Hide all answers   View all answers   Print   Try the Quiz The distance between Station Atena and Station Barcena is 84 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: 1. the bird flies at 80 miles per hour and the speed of the train is 60 miles per hour Answer: 1122. the bird flies at 60 miles per hour and the speed of the train is 80 miles per hour Answer: 72 Solution: Case 1: Bird flies at a speed greater than that of the train 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. Food for thought: How many journeys back and forth does the bird make in Case 1? Would the distances in these back and forth journeys form an infinite series with a finite sum? Wish to try a simple puzzle similar in concept to Case 2? Then click here.   Try the Quiz :     Puzzles & Brain Teasers : The Bird and the Train