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

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

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* n_1 = x_2* n_2`

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

Thus,

`7* 8 = x_2* (1)/(2)`

`56=(x_2)/(2)\implies x_2 = 112`

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

Answer 2

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