<p>Okay, I know Xiggi's equation can be applied to problems in which someone is traveling to and fro a destination with the SAME distance in both trips, or problems where someone is traveling to somewhere and switches the speed halfway there. (essentially all problems that have 2 different average speeds and they both were applied to the same distance) - this equation is (rate1)(rate2)(2)/(rate1+rate2)</p>
<p>I also know that if the distances are DIFFERENT, we can use the logic of - (average speed = total distance traveled/total time taken). For example- Jim travels from point A->B in 3 hrs. For the first hour, he went 40 mph, then he switched to 50mph for the next 2 hrs, what's the avg speed? You can then say that (avg. speed = (140/3). Since 140 is the total distance traveled and 3 is the total time it took.</p>
<p>But, what if you had a problem that asked you this - a man went from home to work at 30 mph and then drove home at 45 mph, the total trip took 3 hours. How long did it take him in minutes to get from work to home? How would you solve that? Or what if that problem asked how far did he travel on each respective trip?</p>
<p>Basically I know how to find average speed, but I need some shortcuts for finding total and respective time and distance. Also, if you have any more types of rate/distance/time problems that I haven't touched on, please share. </p>
<p>My goal is to be 100% prepared when it comes to level 5 problems such as the ones above where I can just plug the numbers into a simple equation without breaking a sweat.</p>
<p>Distance formula: d = r * t
There: d = 30 * (3 - t)
Back: d = 45 * t
Solve for t: 30 * (3 - t) = 45 * t
90 - 30t = 45t
t = 1.2 hours
Convert to minutes: 1.2 * 60 = 72</p>
<p>Distance either the “there” or “back” from above: d = 45 * t
d = 45 * 1.2 = 54 miles
Check by taking the other: d = 30 * (3 - t)
d = 30 * (3 - 1.2) = 54 miles</p>
<p>All distance questions (the hard ones) require you to follow these steps:</p>
<ol>
<li><p>Plug everything into two distance formulas.</p></li>
<li><p>Set like terms equal. (sometimes the distance will be the same and they will give you conditions about the time and the speed)</p></li>
<li><p>Solve.</p></li>
</ol>
<p>Thanks !!! especially Silver Aurora. I love the classic system of equations strategy, but it never crossed my mind to do the (3-t) and t thing… thanks :)!</p>
<p>If you want to answer both questions:
Average speed? 2.30.45/75 = 36 mph
Total distance = 3 x 36 mph
One way = 108 mph / 2 = 54 mph
Time to come home = 54/45 = 1.2 hours or 72 minutes</p>
<p>Total time to answer both question? 15 seconds</p>
<p>**If you only wanted to answer the first part <a href=“How%20long%20did%20it%20take%20him%20in%20minutes%20to%20get%20from%20work%20to%20home?”>/B</a> it is even simpler. </p>
<p>180 x 30/75 or 72 minutes.</p>
<p>No need to WASTE time on those silly equations.</p>
<p>wow from the man himself! thanks a lot :)!! I like both xiggi’s and silveraurora’s strategies! Perhaps if I’m pressed for time, I will quickly use the xiggi method, and if I have extra time I can double check it with the full algebra. Thanks guys, this forum is a LOT of help!</p>
<p>The SAT is not about “double-checking” answers. That is high school stuff. The SAT is about answering the questions correctly and with confidence, and AVOIDING falling in the timesinks traps presented by The College Board. </p>
<p>Why make things more complicated than needed by making it … school like?</p>
<p>I totally get what you mean xiggi. It’s just that in my past 10 years of math experience, I have always had a desire to prove that an answer is correct in as many different ways as possible, it builds my confidence in the answer. Over the next two months I will have taken over 15 full math sections on the SAT, and I’m sure that by then my SAT confidence will be high enough to jump over CB’s hurdles and use the fast equations :)</p>
<p>By the way, I have never gotten to read your guide, xiggi, I really should check to see if it has information like this in it before asking the forum. You’ve always got the fastest method for level 5 math it seems!</p>
<p>xiggi’s strategy can be used on problems in which the two distances in question are equal, which I think applies to ALL problems on the SAT. I’m not sure if this is true, but I don’t think the SAT includes problems like this with two different distances.</p>
<p>Wow I never thought of doing it that way, xiggi! Good method!
When I do SAT math, I always make silly mistakes, so I like check my answers. When I finIsh early, I always go back right to the start of the section and do every question again. And yes, I always find at least one silly mistake. I think that’s my only problem.</p>
