[ Motion Problems ]

Three runners - Anton, Seryozha, and Tolya - are participating in a 100 m race. When Anton finished, Seryozha was 10 meters behind him, and when Seryozha finished, Tolya was 10 meters behind him. At what

| distance from each other were Tolya and Anton when Anton finished? (It is assumed that all boys run at constant, but, of course, not equal speeds.)

#
Notice that Tolya's speed is $9 / 10$ of Seryozha's speed.

## Solution

Since Tolya's speed is $9 / 10$ of Seryozha's speed, by the time Anton finished, Tolya had run $9 / 10$ of the distance covered by Seryozha, which is $90 \cdot{ }^{9} / 10=81 \mathrm{~m}$.

## Answer

$19 \mathrm{~m}$.