Question

the number of hours required to build a fence is inversely proportional to the number of people working on the fence. if it takes 7 people, 19 hours to complete the fence, then how long will it take 11 people to build the fence? (round answer to 2 decimal places if needed)

Answer 1

≈ 12.10 hours

Explanation:

let h be the number of hours and n the number of people.

given h is inversely proportional to n, then the equation relating them is

h =
`(k)/(n)` ← k is the constant of proportionality

given it takes 7 people, 19 hours to complete a fence , then

19 =
`(k)/(7)` ( multiply both sides by 7 )

133 = k

h =
`(133)/(n)` ← equation of proportion

substitute n = 11 into the equation

h =
`(133)/(11)` = 12.0909...

It will take 11 people, 12.10 hours ( to 2 decimal places )