<ol>
<li><p>According to the map, the gas station is 5 km west and 2km south of your house. The post office is 3 km east and 4 km north of your house. How many kilometers apart are the gas station and the post office? (Grid-In)</p></li>
<li><p>If x < 4/z and z < 0, then:
A) x + z < 4
B) x+z < 4
C) x/2 < 4
D) xz < 4
E) xz > 4</p></li>
<li><p>If Ramon can paint a fence in two hours, Jenny can paint the same fence 15 minutes faster than Ramon, and Dennis can paint it in half Ramon’s time, about how many minutes will it take to paint the fence if all three people work together?</p></li>
</ol>
<p>I’m not a veteran 
but I think I can help.</p>
<p>
</p>
<p>Well we know z is a negative because it is less then zero so if we want to move z to the other side we will need to change the < to >.
x < 4/z
xz > 4z/z
xz > 4</p>
<p>^ Correct. Thank you for your contribution!</p>
<p>
</p>
<p>
<a href=“http://i43.■■■■■■■.com/rwq7b8.jpg[/img]”>http://i43.■■■■■■■.com/rwq7b8.jpg
![http://i43.■■■■■■■.com/rwq7b8.jpg[/img]](http://i43.tinypic.com/rwq7b8.jpg%5B/img%5D){kind=link}
</a>
Well, if you can see the diagram, you see the answer is 10. We get to this answer by adding 5 to 3 which makes 8. Then we add 2 to 4 which makes 6. Then we use the Pythagorean theorem to get 10. :)</p>
<p>The last one I’m not sure…</p>
<p>^ Ah, I didn’t even think of that, thanks again!</p>
<p>Oh, and I found the solution to my last problem after trial and error.</p>
<p>Work / Time1 + Work / Time2 + Work / Time3 = Work / Total time</p>
<p>1 / 2 + 1 / 1.75 + 1 / 1 = 1 / 0.48</p>
<p>0.48 x 60 = 29 minutes.</p>
<p>You welcome :)</p>
<p>And thanks for posting the formula for the third… I was curious.</p>
<p>Question 1:</p>
<p>For these, I plotted them on a coordinate plane. (I had north/south be the Y-values, with north as the positive values.) The House was the origin.</p>
<p>The Gas station was 5 to the West and 2 to the south, so its coordinates were (-5,-2).
The Post office was 3 to the East and 4 to the North, so its coordinates were (3,4).
Then I used the distance formula to find the length of the line segment between them.</p>
<p>Can you explain the work for the 3rd one? Because if you add your fractions up, they don’t add up to your numbers… I understand that you set them to terms of hours but I’m confused by the 1/0.48 part.</p>
<p>For that question, I converted how much work each person gets done in 1 min (e.g Ramon gets 1/120 of the fence done per min, J was 1/115, and D was 1/60 per min) and added it up. </p>
<p>I converted this number to a common fraction because I forgot to use my calculator lol and it came out to be 29/840 (the fraction of the work that the 3 of them combined get done per min). So 29/840 * x = 1 (the whole). x = around 29 min like you got.</p>
<p>By the way, 6,8,10 is a multiple of the Pythagorean triple 3,4,5 (just multiply each number by 2). So there is no need tro waste time with the Pythagorean Theorem.</p>
<p>Perhaps a detailed explanation would help readers of this forum better understand how to do problem 3.</p>
<p>So here goes:</p>
<p>If Ramon can paint a fence in two hours, Jenny can paint the same fence 15 minutes faster than Ramon, and Dennis can paint it in half Ramon’s time, about how many minutes will it take to paint the fence if all three people work together?</p>
<p>The units for the rate at which a worker paints fences is defined as fences/minute. So Ramon’s rate is 1/120 fences/minute, Jenny’s is 1/105 fences/minute, and Dennis’s is 1/60 fences/minute.</p>
<p>How many fences can they, working together, paint in m minutes? (m/120 + m/105 + m/60) fences, which is m (29/(56<em>15) fences. We want to paint one fence: so m</em>(29/(56<em>15)) = 1 fence, and m = (56</em>15)/29 minutes which is approximately 29 minutes</p>
<p>x/2 < 4 is true as well.</p>
<p>x must be a negative number, and any negative number divided by 2 will be less than 4.</p>