Algebra help - a race around a regular polygon

In summary, 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, Ernie will have traveled one third of the perimeter of the polygon when they meet.
  • #1
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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  • #2
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?

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  • #3
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.
 
  • #4
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?
 
  • #5
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.
 
  • #6
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, [tex]P = 12x[/tex] meters.

Bert's distance is [tex]\tfrac{2}{3}P.[/tex]
Ernie's distance is [tex]\tfrac{1}{3}P[/tex]

Therefore . . .
 

What is a regular polygon?

A regular polygon is a polygon with all sides and angles equal in measure. It can have anywhere from 3 to infinity sides.

What is algebra?

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols to solve equations and formulas.

How can algebra help in a race around a regular polygon?

Algebra can help in calculating the distance traveled, time taken, and speed of a race around a regular polygon. It can also be used to determine the number of laps or sides of the polygon needed to complete a certain distance.

What are some common algebraic formulas used in a race around a regular polygon?

Some common formulas used in a race around a regular polygon include the perimeter formula (P = ns, where n is the number of sides and s is the length of each side), the interior angle formula (A = (n-2)180/n, where n is the number of sides), and the area formula (A = 1/2nsr, where n is the number of sides, s is the length of each side, and r is the apothem or the distance from the center of the polygon to the midpoint of a side).

What are some tips for solving algebraic problems related to a race around a regular polygon?

Some tips for solving algebraic problems related to a race around a regular polygon include identifying and labeling the given information, using the appropriate formulas, setting up and solving equations, and checking the solution for reasonableness. It is also important to pay attention to units and to round the final answer to the appropriate number of significant figures.

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