Math distance problems.

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1

<p>Of course I know the d=rt formula, and I can do the simple problems. But, I always get stuck on the ones like: (from xiggi)</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>Xiggi gives a formula:
[2<em>Speed1</em>Speed2] / [speed1 + Speed2] or in this case:
2* 8 * 12 / 8 + 12. </p>

<p>But, I realize this is just a manipulation of the d=rt formula, and I find it hard to memorize all these distance equations. Can I solve the above question using d=rt? Can someone give me some advice on how to tackle these problems? Should I memorize these various distance equations?</p>

2

<p>Just use logic. I just remember the following physics formula:</p>

<p>DISTANCE = AVERAGE VELOCITY * TIME
d = vt</p>

<p>Okay, you know the distances are equal, because she’s going from school and then back. And you know that the total time for the round trip is 1 hour.</p>

<p>Let’s solve the formula for t.</p>

<p>d = vt
d/v = t</p>

<p>Remember, the reason we’re solving for t is because we know that the d’s are equal, and because that is the case, we can use algebra. We can’t keep it at vt, because the individual t’s could be differen. All we know is that d<em>fromschool = d</em>tohome, therefore let d be the distance from home to school and from school to home.</p>

<p>Since d/v is equal to t, then you know that d/v + d/v is equal to 1 hour, since the round trip took one hour.</p>

<p>d/8 + d/12 = 1
3d/24 + 2d/24 = 1
5d/24 = 1
5d = 24
d = 4.8</p>

<p>Now, remember, d is equal to one trip. So, the round trip in miles is d + d, or 4.8+4.8 = 9.6 miles.</p>

<p>Just think about it using the simple formula d=vt, don’t bother making or memorizing formulas. This is not a test you can memorize things for.</p>

3

<p>d1 = 8t
d2 = 12(t-1)</p>

<p>Since the distances are the same</p>

<p>8t = 12(t-1)
t = .6</p>

<p>Plugging back in for distance 1
d1 = 8(.6) = 4.8
***Note: this is one way - not the round trip</p>

<p>Because the question is asking for the round trip, multiply by 2
4.8 8 2 = 9.6</p>

4

<p>For these types of problems I was taught to use a table which often simplifies matters:</p>

<p>Okay table fails when posted, but you get the idea?</p>

<hr>

<p>| | Rate | Time | Distance |
|--------------------------------
| To | 8 | x | 8x |
|--------------------------------</p>

<h2>| Back | 12 | 1-x | (1-x)*12 |</h2>

<p>We know:
8x = (1-x) * 12
20x = 12
x = .06</p>

<p>You want the value of</p>

<p>8x + (1-x)*12</p>

<p>So plug in x= 0.6</p>

<p>8(.6) + (1-.6) *12
4.8 + 4.8
9.6</p>