<p>Spill the beans!</p>
<p>Yay! Don't erase anything on your calculator so you can have it after the test!</p>
<p>Haha, the Mod took away the "Official" on our threads lol.</p>
<p>What? That's so lame! =/</p>
<p>I'm guessing this is the place to ask questions?</p>
<p>How do I solve a question like this?</p>
<ol>
<li>Graham walked to school at an average speed of 3 mi an hour and jogged back along the same route at 5 mi an hour. If his total traveling time was 1 hr, what was the total # of miles in the round trip?</li>
</ol>
<p>Not going to post the answer choices, because I want to know how to do it, not make it a big guessing game =) Anyone that knows, help! (hint: the answer is not 4)</p>
<p>I got 7.5 miles...is that right?</p>
<p>I think it's 3.75.</p>
<p>opps, i agree lol</p>
<p>oh snap, how do you do that question...</p>
<p>I<em>Was</em>Here, how did you figure it out?</p>
<p>I got the same answer as I<em>Was</em>Here. The solution is as follows:</p>
<p>Let x and y be the times traveled at 3 miles per hour and 5 miles per hour, respectively. Let us further define the direction of walking at the beginning positive and the return direction negative.</p>
<p>If so, we can model the equation for the total distance traveled as:</p>
<p>3x - 5y = 0 (we know Graham is back at position 0 because he made a round trip).</p>
<p>Furthermore, we know the total time is 1 hour. This yields a second equation:</p>
<p>x + y = 1</p>
<p>Two equations and two unknowns; the problem has been reduced to simply solving a system of linear equations.</p>
<p>If you do not how to do this, first solve for one variable. Let us solve for y.</p>
<p>First, lets multiply both sides of the second equation by 3. We obtain:</p>
<p>3x + 3y = 3</p>
<p>When subtracted from the first equation, we get:</p>
<p>-8y = -3</p>
<p>Which implies:</p>
<p>y = 3/8</p>
<p>y = 0.375</p>
<p>Because we know x + y = 1, it follows that:</p>
<p>x = 0.625</p>
<p>Now that you have the times Graham traveled at each of his different speeds, the solution is simply to add the products of the speeds and the respective times Graham spent in those speeds. Therefore:</p>
<p>3(0.625) + 5(0.375) = 3.75</p>
<p>Which is the answer.</p>
<p>Or you could just follow this formula: ((2)(speed a)(speed b))/(speed a + speed b). In this case, it would be ((2)(3)(5))/(3+5). You get 30/8, which is 3.75.</p>
<p>Interesting. Could you please link to a derivation of that formula? I am intrigued by how it works.</p>
<p>3x=5(1-x) ==>x =5/8
2x3x5/8 =15/4 = 3.75</p>
<p>A completely easy problem that i solved in less than 20 seconds</p>
<p>I solve the prob basically like Ivan.
x/3 + x/5 = 1 (x: the length of the road) => x = 15/8
=> 2x (total # of miles) = 15/4
Right?</p>