Running Around a Circular Well
<p>Let the number of complete laps Laura completes before Tom catches up be \( L \).</p>
<p>Since Tom completes 10 laps while Laura completes 8 laps, the ratio of their speeds is \( \frac{10}{8} = \frac{5}{4} \).</p>
<p>If we set the time taken for Laura to complete \( L \) laps as \( t \), then Tom completes \( \frac{5}{4}L \) laps in the same time, meaning:</p>
<p>1 lap for Tom when Laura completes \( \frac{4}{5} \) laps.</p>
<p>Thus, when they run together, for every 10 laps of Tom, Laura runs 8 laps. Therefore, to find the total laps before Tom catches her:</p>
<p>Set the equation \( 10x = 8(x + 1) \):</p>
<p>\( 10x = 8x + 8 \)</p>
<p>\( 2x = 8 \)</p>
<p>\( x = 4 \)</p>
<p>Hence, Laura completes 4 laps before Tom catches her. The answer is:</p>
<p>4 complete laps.</p>
