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miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle?

Answer :

[tex]\bf \begin{array}{lllllll} tire&\cfrac{1}{6}&\stackrel{\downarrow }{\boxed{\cfrac{2}{6}}}&\stackrel{\downarrow }{\boxed{\cfrac{3}{6}}}&\stackrel{\downarrow }{\boxed{\cfrac{4}{6}}}&\cfrac{5}{6}&\stackrel{\downarrow }{\boxed{\cfrac{6}{6}}}\\\\ cone&&\boxed{\cfrac{1}{3}}&&\boxed{\cfrac{2}{3}}&&\boxed{\cfrac{3}{3}}\\\\ hurdle&&&\boxed{\cfrac{1}{2}} \end{array}[/tex]

notice the overlapping obstacles, bear in mind that 2/6 is really just 1/3 in disguise, just as 3/6 is 1/2 when simplified, and so on.

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