bluecarneal wrote: Anna and Boris move simultaneously towards each other, from points A and B respectively. Their speeds are constant, but not necessarily equal. Had Anna started 30 minutes earlier, they would have met 2 kilometers nearer to B. Had Boris started 30 minutes earlier instead, they would have met some distance nearer to A. Can this distance be uniquely determined? (3 points) Using letter $a,b$ for $A,B$ speeds (km/h) and $d$ as distance, we get : 1) $d\ge \frac a2$ and $d\ge\frac b2$ 2) Meeting point if both starts together is at distance $\frac b{a+b}d$ from B 3) Meeting point if A starts $30$ mn earlier is at distance $\frac b{a+b}(d-\frac a2)$ from B So meeting point is moved $\frac{ab}{2(a+b)}$ towards B. And since this value is symetric versus $a,b$, we get that, in the case where B starts 30 mn earlier, meeting point is moved of exactly the same distance towards A. hence the answer : Yes it can be determined exactly : 2km again.