Problem 7.3. Krosh and Yozhik decided to check who would run faster along a straight road from Kopyatych's house to Losyash's house. When Krosh had run 20 meters, Yozhik had run only 16 meters. And when Krosh had 30 meters left, Yozhik had 60 meters left. How many meters is the length of the road from Kopyatych's house to Losyash's house? (Krosh and Yozhik started running at the same time, each running at their own constant speed.)
Answer: 180.

Solution. When Krosh ran 20 meters, Yozhik ran only 16 meters, so their speeds are in the ratio of $5: 4$.

When Krosh had 30 meters left to run, let him have already run $5 x$ meters (where $x$ is not necessarily an integer). Then by this point, Yozhik had run $4 x$ meters. Therefore, the total length of the entire path in meters is on one side $5 x+30$, and on the other side $4 x+60$. We get the equation $5 x+30=4 x+60$, from which we find $x=30$.

Therefore, the desired length is $5 \cdot 30+30=180$ meters.