ShmoopTube

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Functions as Models, a la Shmoop. Kavi just had his wedding ring stolen.

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That Gollum creep made off with it, and is heading to the Misty Mountains.

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Anyway, Kavi is a world-class triathlete… …and he has 210 kilometers to close the

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gap before Gollum escapes with it forever… In his quest for the ring, Kavi swims for

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2 hours at x kilometers per hour, then bikes for 3 hours at 20x kilometers per hour, and

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finally runs for 2 hours at 4x kilometers per hour…

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…what is his average speed while biking? Here are your choices:

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Kavi has plenty of time to do the math while he’s on his journey.

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He knows that speed equals distance over time. We can rewrite Kavi’s journey as:

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2 times x… plus 3 times 20x… plus 2 times 4x… equals 210…

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…where the first term is his swimming distance, the second term is his biking distance, and

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the third term is his running distance. When we simplify the equation, we get:

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2x plus 60x plus 8x equals 210. So 70x equals 210.

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Divide 70 from both sides, and we see that x is equivalent to 3 kilometers per hour.

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Remember, we’re looking for Kavi’s biking speed, which is 20x…

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So we multiply 20 by our 3 kilometers per hour to get 60 kilometers per hour…

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…and our answer is “E”. As it turns out, Kavi arrives at the same

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answer we did… …just as he catches up with Gollum, and

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wrestles the ring from the creature’s grasp. When he’s done, Kavi throws him into molten

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lava for good measure. Dude’s had a rough week.

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