A troop of scots hiked to the county scout cabin at the rate of 2 miles per hour. They rode back to headquarters at 18 miles per hour. If the round trip took 10 hours, how far is headquarters from the cabin?

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A troop of scots hiked to the county scout cabin at the rate of 2 miles per hour. They rode back to headquarters at 18 miles per hour. If the round trip took 10 hours, how far is headquarters from the cabin?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Let \(x,y\) be the times needed to go up and down respectively. Then \(x+y=10\) and \(\text{distance}=2x=18y\). So \(x=9y\) and hence \(10y=10\). So \(y=1\) and \(x=9\). So the distance of the headquarter from the cabin is \(2x=18\) miles.

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