<p>I can't solve this math problem, and the problem is I don't have the answers.</p>
<p>Bernardo drives to work at an average speed of 50 miles per hour and returns along the same route at an average speed of 25 miles per hour. If his total travel time is 3 hours, what is the total number of miles in the round-trip?</p>
<p>A)225
B)112.5
C)100
D)62.5
E)50</p>
<p>I tried using the equation [2<em>Speed1</em>Speed2] / [speed1 + Speed2] but I got 33.33.</p>
<p>Let the one-way distance be x. Time taken for onward journey = x/50. Time taken for return journey = x/25. Total time = 3 hrs.</p>
<p>Therefore x/50+x/25=3. 3x/50=3. x=50.</p>
<p>Total journey = 2x = 100</p>
<p>Here is how I did it. Easier I think:</p>
<p>If a person goes from one place to another in 25 miles/hr he takes some time. Now if he goes the same distance at 50 miles/hr how much time would he take as compared to before?</p>
<p>Well 50 is double the speed as 25, so he is going twice as fast, so it would take half as much time at 50 miles/hr right? right.</p>
<p>So 3 hours in total, breaking it down in to two you need to get one time that’s double the other, which is 1 and 2.</p>
<p>Now what is 1 ? well we got it from 3 ‘hours’, so its ‘time’, and which speed is it the time for? well its the smaller time, and the smaller time will be when the speed is greater, so its for the 50 miles/hr speed.</p>
<p>How to get distance? multiple speed and time. because speed is ‘distance/time’ when you multiple by ‘time’ the time and time cancel to give you distance. so 50 multiplied by 1, which is just 50. </p>
<p>So what does that mean? it means it took him 1 hour to go 50 miles at the rate of 50 miles/hr. Which as the question says is half of the journey. The distance for the other half will be the same of course, so 50 miles + 50 miles = 100 miles.</p>
<p>@MickyS why take the trouble to draw half-a-page analogy when you have algebra at your disposition, that too which takes a max. of 3 lines.</p>
<p>im not posting a solution as @canhazphysics has already done a great job.</p>
<p>^ @MickyS No no no no, and no.</p>
<p>OP, one simple rule for this type of problem.</p>
<p>Distance / Speed 1 + Distance / Speed 2 = Total time.</p>
<p>Now apply it.</p>
<p>X / 50 + X / 25 = 3. </p>
<p>Solve for X. X is 50. That is the distance from the house to work. We want the entire trip in miles. So, 2X = 50 x 2 = 100.</p>
<p>hey @SirWanksalot why are you pointing towards me. i asked him to use the algebra which you used.</p>
<p>You guys posted at the same time, Akash. He said “^Micky”. Seriously. :/</p>
<p>Lol, don’t ■■■■■ me akashdip.</p>
<p>Woo, you’re already famous for trolling outside the India forum too xD</p>
<p>oh sorry. i didnt notice the @MickyS part. sorry.</p>
<p>and no. im not famous for trolling anywhere.</p>
<p>Well there is a reason they made those speeds 25 and 50, and my analogy is that reason. I wrote it out like that to explain how it works, but practically speaking it takes very very little time to do it that way. </p>
<p>All you need to realize is it would take double the time with 25 than it would with 50, which is common sense. </p>
<p>I know I’m not the only one who functions like this, and that there are more people like me who prefer to solve things in their head using logical approaches than write out algebraic expressions. And you really CAN do it in your head how difficult is 50 x 1 x 2? . I dread solving stuff like X / 50 + X / 25 = 3 given the time restraints.</p>
<p>Given the strain and anxiety of the exam, you are very likely to make a miscalculation in your head. So, it’s better to simply put the equation into your FX calculator, then press Shift and solve. Walla~ You have the value of X. Now times 2. You have your answer.</p>
<p>And don’t forget, not all questions have the same easy numbers. There are some questions in which the distance turns out to be something similar to 13.3333333 or 16.6666667 etc.</p>
<p>is a calculator allowed in a sat math exam??</p>
<p>^ lol, Yes, graphing n scientific both are allowed.</p>
<p>OP – you were actually very close to getting the right answer and very quickly as well. You correctly recognized that this was a time to average two average speeds (using “Xiggi’s formula”). And you did it right – 33.3… is the average HOURLY speed. Now you just have to multiply that by the 3 hours that you were traveling to get 100 miles as your answer. </p>
<p>The other algebraic solutions offered above are fine too, but since you did in fact know the shorter way, might as well use it…</p>
<p>Taking in mind that there are indeed solutions that are more time-friendly than the algebraic ones, I still prefer to have a single formula/equation that applies to the same type of problem. Trust me, this problem is repeated heavily throughout SAT exams. I’ve developed a formula for almost every type of SAT problem there is (besides logical data analysis questions of course). This comes by time. In the November exam, I literally finished each section in 10 minutes. I was doing each problem with minimal effort, simply pasting the equations and plugging in the numbers. It’ll go a long way if you follow this strategy, unless you’d rather improvise during the exam.</p>
<p>Point: memorize this: Distance / Speed1 + Distance / Speed2 = Total time.</p>