Three students are sitting on a school bus. Eli is 4 feet directly behind Bella and 5 feet directly left of Oliver. Eli makes a paper airplane and throws it to Bella. Bella throws the airplane to Oliver, who throws it back to Eli. How far has the paper airplane traveled? If necessary, round to the nearest tenth.
Question
Three students are sitting on a school bus. Eli is 4 feet directly behind Bella and 5 feet directly left of Oliver. Eli makes a paper airplane and throws it to Bella. Bella throws the airplane to Oliver, who throws it back to Eli. How far has the paper airplane traveled? If necessary, round to the nearest tenth.
Solution
To solve this problem, we need to calculate the distances between each pair of students and then add them up.
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The distance between Eli and Bella is given as 4 feet.
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The distance between Bella and Oliver is not directly given, but we know that Bella is directly between Eli and Oliver. Since Eli is 5 feet to the left of Oliver, Bella is also 5 feet from Oliver.
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The distance between Oliver and Eli is not directly given. However, we know that Eli is 4 feet behind and 5 feet to the left of Oliver. We can use the Pythagorean theorem to find the distance between them. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the distance between Oliver and Eli is the hypotenuse, and the distances to the left and behind are the other two sides. So, the distance is sqrt(4^2 + 5^2) = sqrt(16 + 25) = sqrt(41) = approximately 6.4 feet.
So, the total distance the paper airplane traveled is 4 feet (Eli to Bella) + 5 feet (Bella to Oliver) + 6.4 feet (Oliver to Eli) = 15.4 feet.
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