<p><span style="color:#27ae60;"><span style="font-size:20px;">Solving the Problem</span></span></p>
<p>This problem is best solved by going <strong><span style="color:#8e44ad;">Piece by Piece</span></strong>. Let's start reading and making deductions:</p>
<blockquote>
<p>Judy drove 20 miles from her house to a theater at an average rate of 50 miles per hour.</p>
</blockquote>
<p>We can begin by setting up a work-rate equation based on what we know:</p>
<ul>
<li>work done = rate * time</li>
<li>work done = distance travelled by Judy = $20$ miles</li>
<li>rate = speed Judy travelled at = $50$ miles per hour</li>
</ul>
<p>So, now we can solve for the time Judy took to arrive at the theater:</p>
<ul>
<li>time = distance/rate</li>
<li>time = $\frac{20}{50}$</li>
<li>time = $\frac{2}{5}$ hours or $0.4$ hours or $24$ minutes</li>
</ul>
<p>So, we know that Judy took $24$ minutes to drive to the theater.</p>
<blockquote>
<p>Greg drove from his house to the theater in 1/3 of the time it took Judy to drive to the theater,</p>
</blockquote>
<p>If Judy took $24$ minutes to drive to the theater, and Greg took a third of that time, then Greg took $\frac{24}{3} = 8$ minutes to drive to the theater.</p>
<blockquote>
<p>and they both arrived at the theater at the same time. If Judy left her house at 7:30 P.M,</p>
</blockquote>
<p>If Judy left her home at 7:30 pm and took $24$ minutes to arrive at the theater, then she would arrive at 7:54 pm.</p>
<p>Since Greg and Judy both arrived at the same time, Greg also arrived at 7:54 pm.</p>
<blockquote>
<p>when did Greg leave his house?</p>
</blockquote>
<p>We know that Greg arrived at 7:54 p.m. and drove for $8$ minutes, so Greg must have left his house $8$ minutes before 7:54 pm. So, Greg left his house at 7:46 pm.</p>
<p>So, the answer would be <span style="color:#27ae60;">D</span>.</p>