Question

The time to do a piece of work is inversely proportional to the number of men employed. If it takes 4 men to do a piece of work in 5days,how long will it take 25 men?

Answer 1

`19" hours and "12" minutes"`

Explanation:

`"let t represent time and n the number of men"`

`"the initial statement is "tprop1/n`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`t=kxx1/n=k/n`

`"to find k use the given condition"`

`t=5" when "n=4`

`t=k/nrArrk=tn=5xx4=20`

`"equation is "t=20/n`

`"when "n=25`

`t=20/25=4/5" day"=19.2" hours"`

`color(white)(xxxxxxxxxxxx)=19" hours and "12" minutes"`

Answer 2

Let `t` be time, `m` be the number of men, and `k` the constant of variation

Inverse variation can be modeled by:
`tm=k`
Given that in 5 days, 4 men can complete work:
`(5)(4)=k`

`k=20`

To solve for time, when 25 men work:
`t=k/m`

`t=20/25`

`t=4/5`

`t= 4/5" day" or 19" hrs" and 12" mins"`