Noah and his grandfather were returning home from a walk. When they were 800 m away from the house, the grandfather said that he was thirsty. Noah immediately ran home, got a bottle of water, and ran back to meet his grandfather who never stopped walking at a steady pace. How many meters from the house did they meet if noah ran four times as fast as his grandfather walked.

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Given that Noah and his grandfather were returning home from a walk, and when they were 800 m away from the house, the grandfather said that he was thirsty, so Noah immediately ran home, got a bottle of water, and ran back to meet his grandfather who never stopped walking at a steady pace, to determine how many meters from the house did they meet if noah ran four times as fast as his grandfather walked, the following calculation must be made:

200 x 4 = 800 - 200 = 600
300 x 4 = 1200 - 800 - (800 - 300) = 100
325 x 4 = 1300 - 800 - (800 - 325) = -25
320 x 4 = 1280 - 800 - (800 - 320) = 480 - 480 = 0

Therefore, they met 480 meters from the house.

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