Algebra help - a race around a regular polygon

[aileenmarymolon]

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?

 

[I like Serena]

Re: algebra help

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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[aileenmarymolon]

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.

 

[I like Serena]

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.

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?

 

[HallsofIvy]

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.

 

[soroban]

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 . . .