Where am I going wrong on this math question?

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1

<p>Ok, here is the question:</p>

<p>It takes 16 facets 10 hours to fill 8 tubes. How long will it take one facet to fill 8 tubes?</p>

<p>Here's what I do:</p>

<p>I set up a proportion:
16:10 = 1:x</p>

<p>However, the answer key in the book says the proportion should be:</p>

<p>16:10 = x:1</p>

<p>Why is this the correct proportion? I thought that the 16 would have to correspond to the 1 because they both represent the number of facets. If someone could tell me where I am going wrong in this problem, I'd really appreciate it!</p>

<p>THANKS and sorry if this post is confusing,</p>

<p>Robbie</p>

2

<p>The book is wrong: typo.</p>

3

<p>Actually, I don't think it is. If you solve the question with my proportion, the answer you get is messed up.</p>

4

<p>Seems to me both proportions are incorrect.
This should be an inverse proportion:
the fewer faucets ---> the greater the time.
(16)(10) = (1)(x).</p>

<p>Related discussions:</p>

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5

<p>the answer should be 160 hrs</p>

6

<p>Dunno if I did this right, but</p>

<ol>
<li> 16 facets 10 hours 8 tubes equates to 2 facets 10/8 hours and 1 tube</li>
<li> 2 facets 10/8 hours and 1 tube equates to 1 facet 10/16 hours and 1/2 tube</li>
<li> so each facet produce 1/2 tubes per 10/16 hours, whose rate is .5/.63</li>
<li> Using (Rate)(Time) = Job done, (.5/.63)(X)=8 tubes</li>
<li> Solve for X=10?</li>
</ol>

7

<p>THANKS for the help guys!</p>

8

<p>The book is not wrong, there is no typo, you set up your ratio wrongly to where 1 facet is better than 16: think about it: which fills tubes faster, 1 facet or 16 facets? Thus, you have an inverse relationship, so the book is very right (and so is karinasagun): (16)(10)=1(x)</p>