A tenth of a second

A frequent competition, even for amateurs, is long-distance running. The running time was measured with a stopwatch with a precision of one tenth of a second. Two other competitors were diligently overtaking each other in the last metres before the finish, while in the final sprint they covered the last 100 m in a time of 12.3 s. Even though they did not finish completely at the same time, at the finish line they were measured the same time. What maximum distance could there have been between them when they passed through the finish line?

Final Answer:

s =  0.813 m

Step-by-step explanation:

$$\begin{gathered} s_1=100\text{m} \\ {t}_1=12.3\text{s} \\ {t}_2=0.1\text{s} \\ {v}_1=s_1/t_1=100/12.3=\frac{1000}{123}\doteq 8.1301\text{m/s} \\ s=v_1\cdot t_2=8.1301\cdot 0.1=0.813\text{m} \end{gathered}$$

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