Question

Helping a friend out

Answer 1

7.5 hours

Explanation:

let t represent time, l represent length and n represent number of painters.

given t varies directly with l and inversely with n then the equation is

t =
`(kl)/(n)` ← k is the constant of variation

to find k use the condition t = 5 when l = 200 and n = 3 , then

5 =
`(200k)/(3)` ( multiply both sides by 3 )

15 = 200k ( divide both sides by 200 )

0.075 = k

t =
`(0.075l)/(n)` ← equation of variation

when l = 500 and n = 5 , then

t =
`(0.075(500))/(5)` =
`(37.5)/(5)` = 7.5 hours