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 July 5th, 2010, 10:59 AM #1 Newbie   Joined: Jun 2010 Posts: 24 Thanks: 0 Proportion I need a simple way to solve this question. It takes 3 men to dig 2 identical trenches in 5 hours. If all the men work at the same rate, how long will it take 5 men to dig 7 of these trenches? I have solved it this way through the help of an example in the book. Solution First we keep the number of trenches constant No of men --- No of trenches --- No of Hours 3 --- 2 --- 5 1 --- 2 --- 5*3 5 --- 2 --- (5*3)/5=3 Next we keep the number of men constant No of men --- No of trenches --- No of Hours 5 --- 2 --- 3 5 --- 1 --- 3/2=1.5 5 --- 7 --- 1.5*7=10.5 Therefore 5 men will take 10.5 hours to dig 7 identical trenches. I want a simpler solution to this.
 July 5th, 2010, 11:23 AM #2 Math Team   Joined: Apr 2010 Posts: 2,778 Thanks: 361 Re: Proportion Hello Haftakan, $\frac{\mathrm{no of hours(h)} \cdot \mathrm{no of men(m)}}{\mathrm{no of tranches(t)}}$ is constant. In this case $\frac{h \cdot m}{t}=7.5$ In this case. Will this do? Hoempa
 July 5th, 2010, 02:49 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond Re: Proportion (number of trenches per man per 5 hours) * (number of men) * (number of 5 hour periods) = (number of trenches) (2/3) * (5) * (x) = 7.

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# It takes 3 men to dig 2 identical trenches in 5 hours if all the men work at the same rate how long will it take 5 men to dig 7 these tranches

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