## 21. Rue Sainte-Catherine

I was walking with my mother-in-law. We were slowly, at a speed of 3 km/h, walking down Rue Sainte-Catherine in Bordeaux, which, as everyone knows (or maybe doesn't know), is straight. Suddenly, I remembered that I needed to drop a letter in a mailbox located a bit further down the street. Leaving my mother-in-law, who continued her walk calmly, I hurried ahead, and after dropping the letter, I walked back to meet her at the same speed (5 km/h). I clearly remember that I left her alone for only 3 minutes.

How far from the mailbox were we when we parted?
21. Let's choose meters and minutes as units of measurement. Then my speed after I left my mother-in-law is $5000 / 60 = 250 / 3 \, \text{m} /$ min, and my mother-in-law's speed (and our common speed during the walk) is 3000/60 = $50$ m $/$ min. Let $S$ be the point where we parted, $R$ the point where we met again, and $B$ the point where the mailbox is located. The distance my mother-in-law walked in 3 minutes is

$$
S R = 50 \cdot 3 = 150
$$

In this time, I walked the distance

$$
S B + B R = S R + 2 B R = (250 / 3) \cdot 3 = 250
$$

Therefore, $2 B R = 100$ and $B R = 50$. Thus,

$$
S B = S R + R B = 200
$$

So, at the moment we parted, we were 200 meters away from the mailbox.