Question

IF IT TAKES 5 MEN TO DIG A DITCH 10 LONG 1 1/2 HOURS, HOW LONG WOULD IT TAKE 7 MEN TO DIG A DITCH 10 FEET LONG

Answer 1

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,


`\bf 1(1)/(2)+1(1)/(2)+1(1)/(2)+1(1)/(2)+1(1)/(2)\implies \stackrel{total~workhours}{7(1)/(2)}`

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


`\bf \cfrac{7(1)/(2)}{7}\implies \cfrac{\quad (7\cdot 2+1)/(7)\quad }{(7)/(1)}\implies \cfrac{\quad (15)/(7)\quad }{(7)/(1)}\implies \cfrac{15}{7}\cdot \cfrac{1}{7}\implies \cfrac{15}{49}~\approx ~\stackrel{hours}{0.30612} \\\\\\ \textit{which is roughly 18 minutes}`