MHB Algebra help - a race around a regular polygon

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SUMMARY

Bert and Ernie are running around a regular polygon with x sides, each side measuring 12 meters. Bert runs at twice the speed of Ernie, which leads to the conclusion that when they meet, Ernie will have traveled one-third of the perimeter of the polygon. The total perimeter, P, is calculated as 12x meters, making Ernie's distance traveled equal to 4x meters. This problem illustrates the relationship between speed, distance, and time in a circular motion context.

PREREQUISITES
  • Understanding of basic algebraic concepts, specifically speed, distance, and time relationships.
  • Familiarity with the properties of regular polygons and their perimeters.
  • Knowledge of ratios and proportions as they apply to motion.
  • Ability to set up and solve equations based on given conditions.
NEXT STEPS
  • Explore the concept of perimeter calculation for various polygons.
  • Learn about relative speed and how it affects distance traveled in opposite directions.
  • Study the application of algebra in solving motion problems involving multiple objects.
  • Investigate real-world applications of speed and distance in racing scenarios.
USEFUL FOR

Students studying algebra, educators teaching motion concepts, and anyone interested in solving problems involving relative speed and distance in geometric contexts.

aileenmarymolon
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Bert and Ernie are running around a regular polygon with x sides, all of length 12m. They start from the same point and run in opposite directions. If Bert is twice as fast as Ernie, how far will Ernie have traveled when they meet?
 
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Re: algebra help

aileenmarymolon said:
Bert and Ernie are running around a regular polygon with x sides, all of length 12m. They start from the same point and run in opposite directions. If Bert is twice as fast as Ernie, how far will Ernie have traveled when they meet?

Hello and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
Re: algebra help

I don't really know where to begin with this question. I know that Speed=distance / Time and that is about it.
 
Re: algebra help

aileenmarymolon said:
I don't really know where to begin with this question. I know that Speed=distance / Time and that is about it.

Well... what is the circumference of the polygon? (Wondering)

Suppose Ernie runs with a speed of 1 m/s, then Bert runs with a speed of 2 m/s.
How far will they have run after, say, 10 seconds?
After x seconds?
And after 2x seconds?
 
First, if they start at the same time, they will have run for the same time when they meet. Since Bert runs twice as fast as Ernie, he will have run twice as far as Ernie. That means that Bert will have run 2/3 of the way around the track and Ernie 1/3.
 
aileenmarymolon said:
Bert and Ernie are running around a regular polygon with x sides, all of length 12m.
They start from the same point and run in opposite directions.
If Bert is twice as fast as Ernie, how far will Ernie have traveled when they meet?
Bert's speed is twice that of Ermie.
Hence, Bert's distance (for a particular time) is twice that of Ernie.

When they first meet, their total distance is the perimeter, P = 12x meters.

Bert's distance is \tfrac{2}{3}P.
Ernie's distance is \tfrac{1}{3}P

Therefore . . .
 

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