<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?
A)225
b)112.5
c)100
d)62.5
e)50</p>
<p>Can we do this problem by multiplying 3 to 75?</p>
<p>He drives to work twice as fast as he does when he comes home. So, the time (t) is takes for him to drive home is twice as much as it is for him to drive to work. Knowing that, you solve for t:</p>
<p>t+2t=3--------------->t=1</p>
<p>So, he drives for 1 hour to work and 2 hours back. Given Distance=Rate*Time, you solve for the distance to and from given the rate and time:</p>
<p>Going to Distance=(50mi/hr)<em>(1hr)=50 miles
Going from Distance=(25mi/hr)</em>(2 hr)=50 miles</p>
<p>Total Distance = 50+50 = 100 miles</p>
<p>What a ■■■■■; 200+ posts in 5 days.</p>
<p>^who are you referring to?</p>
<p>Hey, good solution poster number 2, however it wasn’t completely clear to me atleast so I’ll try and show you guys two methods as well (one short one long).</p>
<p>METHOD 1: Ratios</p>
<p>Ok first off, I guess you just kind of got to see it, but we know he goes 25 mph and 50 mph on the SAME route, which means the SAME distance. So he would have to travel twice as long going at 25 mph as he would for 50 mph giving us a 2:1 ratio of time spent traveling 25 mph to 50 mph. Ok so then we aslo know he travel a total of 3 hours. That ratio i described a few seconds ago gives us:</p>
<p>time spent 25 mph: 2/3 whole time (3 is gotten by adding 2 and 1 from the initial ratio, and 2 is the same 2 in 2:1)</p>
<p>time spent 50 mph: 1/3 whole time because 1-2/3 is just 1/3</p>
<p>k so that means 1 hr 50 mph and 2 hours 25 mph</p>
<p>So now we convert mph to miles based on hours traveled, so just do like:</p>
<p>1hr(50miles/1hr) = 50 miles
2hr(25miles/1hr) = 50 miles</p>
<p>add em up and u get 100 miles total. </p>
<p>METHOD 2: Algebra</p>
<p>k now u can see an algebraic way if u want
we know it is the SAME route so it is the SAME distance right, so that means the following: 25x = 50y
x is the time spent goin 25 mph and y is time spent going 50 mph.</p>
<p>we also know that the total time is 3 hours so that yields:</p>
<p>x + y = 3</p>
<p>k now just do like substitution or something to solve system of equations, i will do substitution since that is fine:</p>
<p>x=3-y</p>
<p>25(3-y) = 50y
75-25y = 50y
75 = 75y
y = 1 <— time spent going 50 mph</p>
<p>x +1 = 3
x= 2 <— time spent goin 25 mph</p>
<p>So now we convert mph to miles based on hours traveled, so just do like:</p>
<p>1hr(50miles/1hr) = 50 miles
2hr(25miles/1hr) = 50 miles</p>
<p>now again, just add these 2 up and its 100 miles.</p>
<p>holy **** that nerd bernardo has to drive far to go to work! is this guy jumpin the border every day or something or y is he driving 3 hrs</p>
<p>Another method of doing this problem is using this formula:</p>
<p>(2<em>speed 1</em>speed 2)/(speed 1+speed 2)*number of hours round trip took</p>
<p>(2<em>50</em>25)/(50+25)*3</p>
<p>(2500/75)*3</p>
<p>33.3333333*3</p>
<p>100</p>
<p>cool formula man, I tend to forget them so I always like to do it an intuitive way. I guess you can always understand how the formula works and derive it, though.</p>
<p>nice one markalex1, your solution is the easiest and the most time-saving one.</p>
<p>to be honest, i got the problem in less than 10 seconds using my ratios method, but whatever works as long as you get the right answer.</p>
<p>dipole; your first method is the method I used and yes it doesn’t need any time</p>
<p>lol screw that formula.
The time it takes you to understand and do the derivations of the formula isn’t worth it. Simply memorizing the formula won’t do you much good either because things can go wrong if you don’t understand how to apply it.</p>
<p>@Zosilo, haha sorry, didn’t mean to sound like a snob :). I just wanted to put in a new solution that hadn’t already been tried.</p>
<p>hi markalex, um i think zosilo said he liked ur strategy; he didnt say or imply that u sounded like a snob (i dont think). And yea did you get that formula from xiggi thread or something? I tried the formula out myself on a problem, and maybe im just dumb or something, but I used it wrong and got it wrong on a practice problem. So ever since I just decided to stop using formulas that I didnt understand (couldn’t derive) by myself. But once again, whatever works for you.</p>
<p>@dipole, oh oops… now I’m just confused. I thought that Zosilo was being sarcastic when he said: nice one markalex1, your solution is the easiest and the most time-saving one. </p>
<p>Then again, sarcasm is difficult to understand while online, so maybe I was wrong.</p>
<p>haha, i understand bro</p>
<p>Oh yeah haha, I did get that formula from the Xiggi thread :)</p>
<p>markalex1; I am talking seriously man. Believe me. it is not sarcasm :). I really think that your method is the easiest and the fastest; however, when I first saw the question I solved it using dipole’s first method.</p>
<p>Really? Oh wow. Oops. Haha, i don’t really even use my method for these problems :). Like you and some other people used, I used the ratio thing Dipole put up.</p>
<p>If I recall correctly, there’s a long debate you had with some RL tutor about this in that old thread. I’m not gonna argue, but we can settle on the part where you gotta understand the derivations in order to use the formula. :)</p>
<p>V somehow your post is below mine. It was above mine when I made this post.</p>
<p>
</p>
<p>The first rule of using a formula is to understand how it works and why it works. The second one is to know when and how to apply it. The College Board is highly predictable and it pays dividends to have a really easy resource in your arsenal. </p>
<p>
</p>
<p>Well, how would you approach the same problem with a very slight difference?</p>
<p>Bernardo drives to work at an average speed of 37 miles per hour and returns along the same route at an average speed of **23 **miles per hour. If his total travel time is 3 hours, what is the total number of miles in the round-trip?</p>
<p>How long do you estimate it would take to solve this problem without a calculator … and without a formula?</p>