<h3 id="back-link"><a href="/">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.1.6.$ Athletes run in a column of length $l$ at speed $v$. The coach runs towards them with speed $u < v$. Each athlete, when he reaches the coach, turns around and starts running back with the same speed. What is the length of the column when all the athletes turn around?
    </p>

    <h3>Solution</h3>
    <p>
                        <p class="TxtSolutions">   Let us imagine stopping the column, then the coach besides his speed will have the speed of the column directed in the opposite direction. With this relative velocity $v + u$ he will during time
            </p>
            <p style="text-align: center;">
                $$t = \frac{l}{v + u}$$
            </p>
            <p class="TxtSolutions">  will run along the column and equalise with the tail. The head of the column, having turned round, will move with relative velocity $v - u$ and after time
            </p>
            <p style="text-align: center;">
                $$t = \frac{{l}'}{v - u}$$
            </p>
            <p class="TxtSolutions">   where ${l}'$ is the length of the new “column” after overtaking. Then
            </p>
            <p style="text-align: center;">
                $$\frac{{l}'}{v - u} = \frac{l}{v + u}$$
            </p>
            <p class="TxtSolutions">   and the length of the new column
            </p>
            <p style="text-align: center;">
                $$\fbox{${l}' = \frac{v - u}{v + u}l$}$$
            </p>
    </p>

    <h4>Answer</h4>
    <p>
        When all athletes turn around, the length of the new column will be equal to ${l}' = \frac{v - u}{v + u}l$
    </p>


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