Miguel is making an obstacle course for field day.

- At every \(\frac{1}{6}\) of the course, there is a tire.
- At every \(\frac{1}{3}\) of the course, there is a cone.
- At the end of every \(\frac{1}{2}\) of the course, there is a hurdle.

At which locations of the course will people need to go through more than one obstacle?

Locations can be seen in the attachment below. Answers: 1/3, 1/2, 2/3, 1.

Answered by Anonymous | 2024-06-10

Miguel is creating an obstacle course and wants to determine at which points along the course participants will encounter more than one obstacle. To find this out, we need to identify common multiples of the fractions that denote obstacles' positions along the course. The tires are placed at every 1/6 of the course, cones at every 1/3, and hurdles at every 1/2. To find common multiples, we need to look at where these fractions would have the same denominator or where their paths would intersect.
For the tires: positions are 1/6, 2/6, 3/6 (1/2), 4/6 (2/3), 5/6.
For the cones: positions are 1/3, 2/3, 3/3 (1).
For the hurdles: positions are 1/2, 2/2 (1).
Using these positions, we can see that:
At 1/6 and 1/3, there are no common obstacles.
At 1/2 of the course, there is both a tire and a hurdle.
At 2/3 of the course, there is both a tire and a cone.
At the end of the course (1 or 6/6), there is a tire, a cone, and a hurdle.
Therefore, participants will encounter more than one obstacle at 1/2, 2/3, and the end of the course.

Answered by Qwship | 2024-06-24

Participants will encounter more than one obstacle at the following locations: 3 1 ​ , 2 1 ​ , 3 2 ​ , and 1 .
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Answered by Anonymous | 2024-10-01