76. Andrei, Boris, and Sergey were competing in a 100-meter race and started simultaneously. When Andrei finished, Boris was 10 meters behind him, and when Boris finished, Sergey was 10.62 meters behind him. How far was Sergey from Andrei when Andrei finished? (It is assumed that each runs at a constant speed.)
76. Let Andrey run $a$ m per second, Boris $b$ m, and Sergey $c$ m. Andrey ran the 100 m distance in $\frac{100}{a}$ seconds, and during this time, Boris ran 90 m, i.e., he spent $\frac{90}{b}$ seconds. When Boris ran 100 m in $\frac{100}{b}$ seconds, Sergey ran 90 m during this time, so $\frac{100}{b}=\frac{90}{c}$. Therefore, we have $\frac{100}{a}=\frac{90}{b}$ and $\frac{100}{b}=\frac{90}{c}$, from which $\frac{90}{b}=\frac{81}{c}$, so $\frac{100}{a}=\frac{81}{c}$. The last 160
means that if Andrey finished, then Sergey was 19 m behind him $(100-81=19)$