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?
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?