SOLUTION: Linda, Rumi, Liz, Amy, Adam, and Sam ran an 800-meter race. Adam BEAT Liz by 7 meters. Sam beat Linda by 12 meters. Adam finished 5 meters AHEAD of Amy but 3 meters BEHIND Sam. Rum

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Question 1177642: Linda, Rumi, Liz, Amy, Adam, and Sam ran an 800-meter race. Adam BEAT Liz by 7 meters. Sam beat Linda by 12 meters. Adam finished 5 meters AHEAD of Amy but 3 meters BEHIND Sam. Rumi finished HALFWAY between the first and last woman. In what order did the women finish? What were the distances between them?
Found 2 solutions by CPhill, MathTherapy:
Answer by CPhill(1987)   (Show Source): You can put this solution on YOUR website!
Let's break down the race results step-by-step.
**1. Adam, Liz, and Amy**
* Adam beat Liz by 7 meters. This means when Adam finished, Liz had 793 meters left.
* Adam finished 5 meters ahead of Amy. This means when Adam finished, Amy had 795 meters left.
* Therefore, Adam finished first among these three.
**2. Sam and Adam**
* Adam finished 3 meters behind Sam. This means when Sam finished, Adam had 797 meters left.
* So Sam finished first overall.
**3. Sam and Linda**
* Sam beat Linda by 12 meters. This means when Sam finished, Linda had 788 meters left.
**4. Order of Finish (Overall)**
* Sam
* Adam
* Amy
* Liz
* Linda
**5. Distances at Finish**
* **Sam:** 800 meters
* **Adam:** 797 meters (3 meters behind Sam)
* **Amy:** 795 meters (5 meters behind Adam, 5 meters from finish)
* **Liz:** 793 meters (7 meters behind Adam, 7 meters from finish)
* **Linda:** 788 meters (12 meters behind Sam, 12 meters from finish)
**6. Rumi's Position**
* The first woman was Amy.
* The last woman was Linda.
* Amy finished at 795 meters.
* Linda finished at 788 meters.
* Rumi finished halfway between them: (795 + 788) / 2 = 1583 / 2 = 791.5 meters.
**7. Women's Order and Distances**
* **Amy:** 795 meters
* **Rumi:** 791.5 meters
* **Liz:** 793 meters
* **Linda:** 788 meters
**8. Correcting Women's Order**
* The women must be ordered according to who finished first.
* Amy finished at 795 meters.
* Liz finished at 793 meters.
* Rumi finished at 791.5 meters.
* Linda finished at 788 meters.
**Final Women's Order and Distances**
* **Amy:** 795 meters (5 meters from finish)
* **Liz:** 793 meters (7 meters from finish)
* **Rumi:** 791.5 meters (8.5 meters from finish)
* **Linda:** 788 meters (12 meters from finish)
**Distances Between Women**
* Amy and Liz: 2 meters
* Liz and Rumi: 1.5 meters
* Rumi and Linda: 3.5 meters
**Final Answer**
The women finished in the following order:
* Amy
* Liz
* Rumi
* Linda
The distances between them at the finish were:
* Amy and Liz: 2 meters
* Liz and Rumi: 1.5 meters
* Rumi and Linda: 3.5 meters
Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
Linda, Rumi, Liz, Amy, Adam, and Sam ran an 800-meter race. Adam BEAT Liz by 7 meters. Sam beat Linda by 12 meters. Adam finished
5 meters AHEAD of Amy but 3 meters BEHIND Sam. Rumi finished HALFWAY between the first and last woman. In what order did the women
finish? What were the distances between them?

That "person"/THING is WRONG!

Participation Order:
1: Sam
2: Adam  - 3 m behind Sam
3: Amy   - 5 m behind Adam, and 8 (3 + 5) m behind Sam 
4: Liz   - 7 m behind Adam, and 2 (7 - 5) m behind Amy 
   Linda - 12 m behind Sam, and 2 [(12 - (2 + 5 + 3)] m behind Liz

Now, with Rumi finishing HALFWAY between the first and last woman (assumed to be Amy and Linda, considering Sam is male),
Rumi would finish HALFWAY between the SUM of the distances between Amy and Linda, or  =  = 2 m

2 m between Amy and Linda is actually Liz’ position. So, it appears that Rumi and Liz came up TIED for 4th.

Assuming Sam is male, and Rumi is female, then it’s:
3rd: Amy
4th: Liz and Rumi (TIED), and 2 m behind Amy
6th: Linda - LAST, and 2 m behind 4th-place TIED runners, Liz and Rumi
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