<p>Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?</p>
<p>I had this question that i had a problem with i looked it up and found out what the answer was and the formula for average rate that is speed 1<em>speed 2</em>2 / speed 1 + speed 2 </p>
<p>But for the life of me i have no idea what it means. if you use this formula you get 36 (not 18 as you should) and for some reason people used it without multiplying the speeds by the 2.</p>
<p>If someone could explain simply what this formula finds (what does it mean that it finds the average rate?) and why you dont multiply by 2 in this specific question it would be great. Thank you.</p>
<p>Don’t think in terms of “formulas” – the problem can be done alone with some intuition. Suppose Esther drives d miles to work, and d miles from work. Using distance = rate*time <–> time = distance/rate, we have</p>
<p>Not sure what you mean by “some intuition.” The SAT requires knowledge and mental agility. In this case, this problem is solved EASILY by following a very simple rule.</p>
<p>Let me share something. What does TCB expects from unprepared students? Easy answer is that they expect and hope such students to fall into the trap of following the loose HS procedure and start working through the timesink of the “Using distance = rate*time” which is none other than a … formula! Just happens to be the most basic and most unhelpful formula to apply for this SAT problem when it shows up. </p>
<p>As far as the question from the OP. The “answer” of 36 is the number for 36 miles per hour. For a round trip of one hour, that means that a round trip is 36 miles. Hence a question about how long did the the DRIVE takes, it is one half the round trip or 18. </p>
<p>While formulas are really helpful on the SAT, it still requires to READ the problem carefully.</p>
<p>Sorry for the confusion, I simply meant, don’t try to blindly apply a formula unless you are sure it works. I find it easier to just set up the equation to find d.</p>
<p>A quick check – if 36 miles indeed was correct, then since her return trip is at 30 mph, it would take her over an hour for the return trip. Since the total roundtrip time is 1 hr, this cannot possibly be correct.</p>