<p>Graham walked to school at an average sspeed of 3 miles an hour and jogged back along the same route at 5 miles an hour. if his total traveling time was 1 hour , what was the total number of miles in the round trip?</p>
<p>I forgot how to do this i remember eeing this somewhere on the forums</p>
<p>I know the key is that Its the same direction or something</p>
<p>CAN someone explain me this in a way that i wont forget?? </p>
<p>Thanks !!</p>
<p>Time = 1 hour
Time Graham took to get to school: x
Time it took him to to get back 1-x</p>
<p>d =st. speed 1 (x) = speed 2 (1-x) since the distance is the same either way.</p>
<p>3x = 5-5x
x = 5/8 hour.</p>
<p>Then you plug the time back in and find the distance. 3(5/8) + 5(3/8)</p>
<p>If you have trouble understanding how I arrived at the answer. Draw two horizontal lines, one on top of the other. Label the first one 3(x) and the second 5(1-x) and it should be pretty clear. Hope this helped you out.</p>
<p>The above is INCORRECT!</p>
<p>At the very last line saying that the distance is 3<em>(5/8)+5</em>(3/8). Actually this is the distance of going BOTH ways (double the distance from the school to the home)</p>
<p>If you want to calculate the distance from the school to the home you need to EITHER calculate 3<em>(5/8) OR 5</em>(3/8).</p>
<hr>
<p>I think this may be what the OP was looking for. Post #25 on: <a href="http://talk.collegeconfidential.com/sat-preparation/68210-xiggis-sat-prep-advice-40.html?highlight=distance+problem%5B/url%5D">http://talk.collegeconfidential.com/sat-preparation/68210-xiggis-sat-prep-advice-40.html?highlight=distance+problem</a></p>
<p>"After spending time building the blocks of knowledge and confidence, students should start developing techniques to save time. The SAT is mostly a test of mental quickness. People who like to solve puzzles tend do well. One good facet of the SAT is that the “puzzles” thrown at students are rather simple and very often repeated. </p>
<p>Again, there are no great secrets. Dedicated students should be able to learn the techniques, leave the calculator in its case, and know what NOT to do. Developing time saving techniques will help students find not only the correct answer, but the best answer in the shortest amount of time. It is worth remembering that the four incorrect answers do NOT matter: nobody needs to show the steps and confirm the answer. Well, that is fine and dandy, but does one acquire the techniques? This is where your source books come in play. As we know, the books contain a number of tips and strategies. While most of the advice is helpful, it is important to tailor it to the individual student. In other words, by reading the various “industry” offerings, a student can acquire a set of tools that will start the process. However, the advice is really aimed at helping average students improve their scores. I am not saying this is a pejorative way! Most books –and organized classes- are most helpful for students who will score between 500 and 650. Despite being incomplete, the advice is still valid and will help anyone in the earlier phases. Concepts such as the process of elimination (POE) and plugging key numbers represent key components of any student’s arsenal. However, to really push your talent to the limit, you’ll have to graduate from the generic concepts. This is accomplished by practicing and looking for hidden patterns. Slowly but surely, your brain will recognize the questions and the answers will “flash” right in front of you. Oh, I know that someone said that the SAT was super easy because ALL the answers are always in front of you –except for the Student Produced Responses or grid-in questions. That is, however, not what I meant! </p>
<p>So, let’s depart from the sterile theory part and look at a few examples of the difference between following the generic advice and moving up to the next step. </p>
<p>For instance In the very beginning of a book published by Princeton Review, we find this strategy: </p>
<p>To follow the example, you need to visualize a square ABCD, and inscribed inside the square a half circle CFD. The half circle diameter is also CD. In this case, the value of the side is 8. This is a very common SAT problem and PR asks the student to identify the area represented by the square MINUS the half circle. </p>
<p>The 5 proposed answers are: </p>
<p>A. 16 - 8 Pi (Pi for [greek]p[/greek])
B. 16 - 16 Pi
C. 64 - 8 Pi
D. 64 - 16 Pi
E. 64 </p>
<p>This is what PR proposes: We know that the value of Pi is a little more than 3. Let's replace Pi with 3 in the proposed answers. Choice A and B are negative numbers. From here, you could guess C, D, or E and it is a guess we SHOULD take. However, we can also eliminate E because 8*8 is 64 and represents the whole square. What do we end up with? A one-in-two shot of getting this problem right. Neat, huh! </p>
<p>Well, not so fast Princeton Review …</p>
<p>Let's look at the problem. How fast can we solve it? </p>
<ol>
<li>Area of square? 8*8 = 64 .... 5 seconds </li>
<li>Area of half circle? Any student sitting for the PSAT or SAT should be able to play with the formulas for areas of circles, squares, and triangles. In this case, the 1/2 circle has a diameter of 8, hence the area of the 1/2 circle should be radius^2 * Pi * 1/2. The answer is 16 Pi/2 or 8 Pi. Time to compute this ... 15 seconds </li>
<li>Guess what? The answer to the question is 64 - 8 Pi. Now you are able to mark answer C with complete confidence, and only after about 25 seconds! </li>
</ol>
<p>What is bad about the PR method? First, if forces the student to attempt FIVE calculations. Despite being mostly trivial, it introduces potential errors. With the building pressure, most students DO make careless mistakes; calculating 16 times 3 easily falls in the category of easy mistakes. Let’s assume that the student does not make a single error and gets it done rather quickly ... at the end, he still has TWO choices or a 50/50 chance. It could mean a plus 1 or a ...MINUS 0.25 in his tally, or a swing of 1.25! </p>
<p>Why do I consider this particular message to be wrong? It tells the student to forego attempting to solve a problem that most 7th graders can solve FAST and CORRECTLY. It also reinforces the idea that the test is all about gimmicks and tricks. While the POE taught by PR is a GOOD technique, I do not quite understand why they selected this problem to illustrate their method.</p>
<p>The next one involves a perennial favorite problem on the SAT: the average rate of speed. Here’s the problem: </p>
<p>A girl rides her bicycle to school at an average speed of 8 mph. She returns to her house using the same route at an average speed of 12 mph. If the round trip took 1 hour, how many miles is the round trip. </p>
<p>A. 8
B. 9 3/5
C. 10
D. 11 1/5
E. 12 </p>
<p>PR offers this solution: First the problem is a hard problem (level 5). TCB assumes that the common student will not attempt to solve the problem and pick the trick answer of 10 since it represents the average of 8 and 12. The common student second choice will be to pick a value that is stated in the problem: 8 or 12. PR provides the strategy to eliminate those Joe Blogg answers. Again, the conclusion of PR is to end up with two choices and pick between B and D. In their words, the student will be in great shape! </p>
<p>What's my issue with this? In my eyes, a 50-50 chance is really not good enough. When you consider how this problem can be solved, the recommendation to guess becomes highly questionable. </p>
<p>What could a student have done? Use a simple formula for average rates -an opportunity that PR strangely forgets to mention. Is this formula really complicated? I could detail the way I developed it while working through similar problems, but the reality is that millions of people have seen it before. I’m absolutely convinced that many good tutors teach it, but you won’t find it in the typical help book. Here it is: </p>
<p>[2<em>Speed1</em>Speed2] / [speed1 + Speed2] or in this case:
2* 8 * 12 / 8 + 12. </p>
<p>Most everyone will notice that the answer is 2*96/20 or simply 96/10. This yields 9.6 or 9 3/5. The total time to do this, probably 20-45 seconds. Not a bad method to know! </p>
<p>It does get better. How would I solve it? </p>
<ol>
<li><p>Check the problem to make sure we have a ONE hour unit. Most often, the SAT writers will use a one hour limit and not a different number of hours. </p></li>
<li><p>As soon as I verify that the unit is 1 hour, I will mark B because I know that the answer is ALWAYS a number slightly BELOW the straight average. It takes only a few problems OF THAT TYPE to realize that it ALWAYS works. </p></li>
<li><p>My total time including reading the problem: about 10 seconds!
Here you have it: two methods that are faster and are bound to yield the correct answer and a healthy dose of self-confidence!</p></li>
</ol>
<p>Obviously, two examples do not tell the entire story. It does, however, reinforce that the SAT is not a test that can reduced to simple tricks. Too many students spend more time looking for quick shortcuts than working on the test itself. For some reason, they believe in a SAT Holy Grail, a mystical summary of tricks that will deliver perfect scores. </p>
<p>As I will repeat often, I do not pretend to know everything about the SAT. I've spent enough time on the SAT to know what works well and what does not work that well. There are merits to a number of strategies, and one has to TRY them in earnest. One of the biggest misconceptions is that the use of strategies represents a shortcut for PREPARATION TIME. Nothing could be further from the truth. The strategies only work for people who invest an adequate amount of time in troubleshooting the techniques and ascertain the relevance to their individual case."</p>
<p>*The above is INCORRECT!</p>
<p>At the very last line saying that the distance is 3<em>(5/8)+5</em>(3/8). Actually this is the distance of going BOTH ways (double the distance from the school to the home)</p>
<p>If you want to calculate the distance from the school to the home you need to EITHER calculate 3<em>(5/8) OR 5</em>(3/8).*</p>
<p>
[quote]
if his total traveling time was 1 hour , what was the total number of miles in the round trip?
[/quote]
</p>
<p>Find 412 / 18 (it's q.18 on p.412 in the Blue Book) inConsolidated List of Blue Book Math Solutions, 3rd ed.</p>
<p>Oh, now a I saw it! Normally they ask about the distance in one direction not in both. Weird. Sorry.</p>