From his home, Latrell would have to walk 8 kilometers north to get to his friend Steve's house and 2 kilometers east to get to his friend Tanvi's house. One day, Latrell walked from his home to Tanvi's house. Together, Tanvi and Latrell cut directly through the field that separated them from Steve's house. When they finished playing at Steve's, Latrell walked back home. In all, how far did Latrell walk? If necessary, round to the nearest tenth.
Question
From his home, Latrell would have to walk 8 kilometers north to get to his friend Steve's house and 2 kilometers east to get to his friend Tanvi's house. One day, Latrell walked from his home to Tanvi's house. Together, Tanvi and Latrell cut directly through the field that separated them from Steve's house. When they finished playing at Steve's, Latrell walked back home. In all, how far did Latrell walk? If necessary, round to the nearest tenth.
Solution
To solve this problem, we need to calculate the total distance Latrell walked.
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First, we calculate the distance from Latrell's house to Tanvi's house, which is given as 2 kilometers.
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Then, we need to calculate the distance from Tanvi's house to Steve's house. This is not given directly, but we know that Steve's house is 8 kilometers north of Latrell's house and Tanvi's house is 2 kilometers east of Latrell's house. This forms a right triangle, with the distance from Tanvi's house to Steve's house as the hypotenuse. We can use the Pythagorean theorem (a² + b² = c²) to calculate this distance.
a = 8 (distance from Latrell's to Steve's house) b = 2 (distance from Latrell's to Tanvi's house)
c = sqrt(a² + b²) c = sqrt(8² + 2²) c = sqrt(64 + 4) c = sqrt(68) c = approximately 8.2 kilometers
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Finally, we add the distance from Steve's house back to Latrell's house, which is 8 kilometers.
So, the total distance Latrell walked is 2 kilometers (to Tanvi's house) + 8.2 kilometers (from Tanvi's house to Steve's house) + 8 kilometers (from Steve's house back to his own house) = 18.2 kilometers.
Therefore, Latrell walked a total of 18.2 kilometers.
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