## E_S_J_F one year ago can someone help me with this question:

1. E_S_J_F

2. anonymous

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3. anonymous

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4. anonymous

But I don't know how to put it in logic yet. :)

5. phi

This one seems tricky. 1. The first key is that the runners are moving at constant rates. 2. we notice that when they meet the first time, the sum of their arcs is 1/2 of a circle, or in angular measure pi radians 3. Based on this info, the two runners are "closing" at a rate of pi radians per unit time. (we have to define our unit time... ) 4. From that first meeting to their second meeting, the sum of their arcs is a full circle, or 2 pi radians. 5. We deduce from items 3 and 4 that it takes them 2pi/pi = 2 "unit times" to travel 1 full circle. in other words, from meeting 1 to meeting 2 it takes 2 unit times We can say Karen ran 131 meters in one "unit time" and in radians, 131/r radians per unit time Andrea is running at pi - 131/r radians per unit time 6. Andrea travels at a rate of $$\pi - \frac{131}{r}$$ rads per unit time times 2 unit times = the radian measure of 158/r $\left( \pi - \frac{131}{r}\right)2 = \frac{158}{r}$ solve for r , $r= \frac{210}{\pi}$ and the circumference is 2$$\pi$$r= 420 meters