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If 6 men dig 9 holes in 10 hrs, how many holes will 10 men dig in 4 hrs if they work at the same rate?

We have 6:9:3 and 10:x:4. I formed two equations, $\frac{9}{6}=\frac{x}{10}$ which gives me $x=15$ and $\frac{3}{9}=\frac{4}{x}$ which gives me $x=12$. I expected to get the same result from both equations. How do I solve this kind of problem?

Gerry Myerson
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maume
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    6 men dig 9 holes in 10 hours means a man digs 1.5 holes in 10 hours. Can you take it from here? – mlc Mar 07 '17 at 07:01
  • no, still in the dark – maume Mar 07 '17 at 07:10
  • Why do you have two sets of equations. The first equation does take time into account and the second doesn't take number of men into account. You need an equation that take holes,men, and time into account at once. – fleablood Mar 07 '17 at 07:47
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    "So we have 6:9:3 and 10:x:4" no. You have no such thing at all. You have $9:6\times 3$ and $x:10\times 4$. Btw is it 10 hours or 3 hours? – fleablood Mar 07 '17 at 07:53
  • Answer these questions, in order (NOT by grabbing a formula, but by thinking about what's actually going on): 1. how many holes will 60 men dig in 10 hours? 2. how many holes will 10 men dig in 10 hours? 3. how many holes will 10 men dig in 20 hours? 4. how many holes will 10 men dig in 4 hours? – Gerry Myerson Mar 07 '17 at 08:14
  • Sixty “men-hours” make nine holes. Now fourty men-hours will make two thirds of nine holes, that is six holes. – Michael Hoppe Mar 07 '17 at 11:13
  • my thinking was totally off on this one, thanks for guidance – maume Mar 07 '17 at 13:54
  • Just to be sure, is the answer 6? – maume Mar 07 '17 at 14:10

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Hint: Essentially, what you need to do is find the rate of each individual man. In other words, you need to figure out how many holes each man digs per hour. As mentioned in mlc's comment, 6 men digging 9 holes in 10 hours means 1 man digs 1.5 holes in 10 hours. Then the question is this: How many holes does this man dig in one hour?

BSplitter
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