Question

If it takes 7 people a total of 8 days to dig a ditch, how many people would it take to dig the ditch in half a day?

Answer 1

It takes 7 people during 8 days to complete 1 job.
If I increase the number of people (for the SAME job) then the number of days will decrease.
I conclude that number of people and number of days are inversely proportional:

x (people)/7 (people) = 8 day/0.5 (day)

x = (8)(7)/0.5 = 56/0.5 = 112 people

Answer 2

Answer: 112 people would it take to dig the ditch in half a day.

Step-by-step explanation:

Since, if $x_1$ people do a work in $n_1$ days and the same work is done by $x_2$ people in $n_2$ days,

Then we can write,

$x_1\times n_1 = x_2\times n_2$

Here, $x_1$ = 7, $n_1$ = 8 days, $n_2$ = 1/2 days ( Half of a day),

Thus,

$7\times 8 = x_2\times \frac{1}{2}$

$56=\frac{x_2}{2}\implies x_2 = 112$

Hence, 112 people would it take to dig the ditch in half a day.