Motion Around a Circular Track
<p>Let the circular track be of circumference C. Tom completes 10 rounds, which means he covers a distance of 10C.</p>
<p>Laura completes 8 rounds, which means she covers a distance of 8C.</p>
<p>The speeds of Tom and Laura can be represented as:</p>
<p>Speed of Tom = 10C/t</p>
<p>Speed of Laura = 8C/t</p>
<p>In order to find how many complete rounds Laura makes before Tom reaches her, we can set up the equation:</p>
<p>Speed of Tom = Speed of Laura + distance covered by Laura in time t.</p>
<p>Let x be the number of complete rounds Laura runs before Tom catches up with her, which can be expressed as:</p>
<p>10C/t = 8C/t + (xC/t).</p>
<p>Solving for x:</p>
<p>10 = 8 + x,</p>
<p>x = 2.</p>
<p>Thus, Laura will have completed 2 complete rounds before Tom reaches her for the first time.</p>
