<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-relative-speed" target="_blank">Relative Speed Exercise</a></p><p><span style="color:#27ae60;">Relative Speed</span> is an interesting phenomenon that can sometimes defy our intuition. It refers to one's speed RELATIVE (in comparison) to some other speed. Imagine you're driving on the highway at $70$ mph and there is a car right next to you driving the EXACT SAME speed. In that case, what is your speed relative to that car? It's $0$!</p>
<p><strong><span style="color:#8e44ad;">Two Rules to Remember</span></strong>:</p>
<p style="margin-left: 40px;"><strong>Rule 1</strong>: If two people, or cars, or some other entities are moving in OPPOSITE directions, you add the speeds.</p>
<p style="margin-left: 40px;"><strong>Rule 2</strong>: If two people, or cars, or some other entities are moving in the SAME direction, you find the difference in the speeds.</p>
<p><strong><span style="color:#8e44ad;">Example 1</span></strong></p>
<p>John is driving toward Bill at $80$ mph and Bill is driving toward John at $70$ mph. If they are $300$ miles apart, how long will it take for them to meet?</p>
<p>Because they're driving in opposite directions (toward each other), we add the speeds to get a relative speed of $70 + 80 = 150$. This is the rate we use in the equation $d=rt$.</p>
<p>$$300 = 150t$$</p>
<p>$$t = 2 \ hours$$</p>
<p><strong><span style="color:#8e44ad;">Example 2</span></strong></p>
<p>John is riding his bicycle on a circular track at a constant speed of $9$ meters per second. Bill is $400$ meters in front of John and is riding his bike at a constant rate of $5$ meters per second. How long will it take for John to catch up to Bill?</p>
<p>Because they're riding in the same direction, we subtact the lower speed from the greater to get $9 - 5 = 4$. This is the rate in our $d=rt$ equation.</p>
<p>$$400 = 4t$$</p>
<p>$$t = 100 \ seconds$$</p>