I wasn't going to click on this one, but the all-caps enthralled me and hypnotized me.
so the 5 men do the ditch in 1 and 1/2 hours, that means, each men worked 1 and 1/2 hours, now, we have 5 men, let's add all the "workhours" and is,
[tex]\bf 1\frac{1}{2}+1\frac{1}{2}+1\frac{1}{2}+1\frac{1}{2}+1\frac{1}{2}\implies \stackrel{total~workhours}{7\frac{1}{2}}[/tex]
now, we know that is the total workhours do the the 10 feet ditch, what about 7 men doing it? well, the 7 men will have to cover those workhours, meaning each one will work
[tex]\bf \cfrac{7\frac{1}{2}}{7}\implies \cfrac{\quad \frac{7\cdot 2+1}{7}\quad }{\frac{7}{1}}\implies \cfrac{\quad \frac{15}{7}\quad }{\frac{7}{1}}\implies \cfrac{15}{7}\cdot \cfrac{1}{7}\implies \cfrac{15}{49}~\approx ~\stackrel{hours}{0.30612}
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\textit{which is roughly 18 minutes}[/tex]
