# Today's CB Question of the Day

<p>If it takes 10 people 12 hours to do a certain job, how many hours would it take 6 people, working at the same rate, to do 1/4 of the same job?</p>

<p>A. 6
B. 5
C. 4 1/2
D. 4
E. 3 3/4</p>

<p>The answer is B, which I completely understand how to get. My question is this: why does a simple proportion not work for this type of problem? At first I did:
10/12 = 6/x, got x = 36/5, then multiplied that by 1/4, which gets me 1.8. This answer isn't even an option. Then I thought it through and got 5, but I still wonder: why isn't it just a proportion?</p>

<p>it's inversely proportional not directly proportional</p>

<p>I don't quite understand the way CB did it either. I got 1.8 at first too! :)</p>

<p>and.. isn't there a really quick, simple way to go about "work" problems? I remember seeing it somewhere....</p>

<p>12(10)=6(x)</p>

<p>12(10)=6(x)</p>

<p>^^---^^
That answer yields x = 20 :(</p>

<p>This is the fastest way to do it:</p>

<p>Total Work = 12 * 10 = 120
1/4 of same work = 120/4 = 30
Hours needed with 6 workers = 30/6 or 5 </p>

<p>B is answer. </p>

<p>PS You may want to create equations, but simply writing a diagram of the problem would work equally well.</p>

<p>xiggi, what's wrong with the answer of x = 20? They asked how long it would take them to do 1/4 of the same job, so it would be 1/4*20 which is the correct answer 5. That seems faster to me then the second way you did it, although they're both good.</p>

<p>both are the same proccess--except with x=20, you have to then divide by 4.</p>

<p>If you set an equation up, the answer should be equal to x. The equation 12(10)=6(x) is incomplete since you still need to incorporate the 1/4. If you wanted to write the equation correctly, you should write
(12*10)/4=6x </p>

<p>Imprecision and incompleteness on the SAT cause the errors we later call silly and stupid. </p>

<p>PS Note how the equation (12*10)/4=6x is EXACTLY the same as the method I showed. :)</p>

<p>Lol</p>

<p>(10/12)*6 = 5</p>

<p>n00bs. :)</p>

<p>Gumball, try your method with this problem:</p>

<p>If it takes 10 people 10 hours to do a certain job, how many hours would it take 6 people, working at the same rate, to do 1/4 of the same job?</p>

<p>Is the answer (10/10)*6 = 6 ?</p>

<p>Personally the easiest way for me to understand it by inverse proportion is:</p>

<p>xy=k
(10)(10)=k
k=100
6y=100
y=16.6667 -> /4 -> 4.167</p>

<p>If the last question was on the SAT, I would write down 25/6</p>

<p>(10*10)/4 = 25
With six people => 25/6</p>

<p>i don't get it,</p>

<p>patwu89 said it was indirectly proportional, while xiggi did it the direct proportional way? In brief could someone tell me what both those mean and how to apply it?</p>

<p>think of it as this:
since 12 persons take 10 hours to complete it, 1 person does 1/120 of the work in 1 hour.
ergo 1/120 times 6 =1/20 (each person has to do only 1/20 of the work)
(1/4)/(1/20)=5 (1/4 of the total work will need one to work for 5 hours)</p>