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23. Bea Debest, Ima Slo, and Betsy Luzes run in a 200 meter rce. When Bea crosses the finish line, Ima is 10 m behind Bea. when Ima crosses the finish line, Betsy is 10 m behind Ima. If all 3 runners ran at a constant speed, how far was Betsy from the finish line when Bea won the race?

All are in meters.

A.18
B.19
C.19.5 ANSWER
D.20
E.21.5
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[unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] Find x+y.
Ans 1/2

Thank you

Wait the answer is 3???
I don't get it...My answer is valid...I used my 89 to check.

If you do [1,2;0,.5]^-1 you get [1,4;0,2]

When Bea finishes, she is at 200 meters and Ima is at 190. Their speeds must be in a ratio 20/19. The same is true of Ima compared to Betsy, so Betsy's speed compared to Bea's is 19^2/20^2. When Bea is at 200m, Betsy's position will be this ratio * 200m which gives 361/2=180.5.

Thus C

You have two distance equations with runners a, b, and c and 2 different times. First is the first time, [unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula] or [unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

Plugging in the first value into the second equation we get

[unparseable or potentially dangerous latex formula]

Now do the same thing again for the second two runners, you'll get the same thing.

[unparseable or potentially dangerous latex formula]

Substituting in the equation we had for [unparseable or potentially dangerous latex formula] we get

[unparseable or potentially dangerous latex formula]

Now we want to find the distance [unparseable or potentially dangerous latex formula] traveled at [unparseable or potentially dangerous latex formula]. Use the distance formula.

[unparseable or potentially dangerous latex formula]

If you recall from our very first equation we know that [unparseable or potentially dangerous latex formula], so plugging that in we get

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

Uups, look like I got beat to the punch, oh well.