Question 1177642
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