Question

The time it takes to remodel a kitchen t(p) varies inversely with the number of workers assigned to the job p. A kitchen remodeling job takes 40 hours to complete when 2 workers are assigned to it. Which equation can be used to find the time to complete the job when p workers are assigned to it.

A. t(p)=40p
B. t(p)=8p
C. t(p)=80/p
D. t(p)=20/p

Answer 1

t(p) = 80/p is the answer.

Answer 2

Answer: C.
`t(p)=(80)/(p)`

Explanation:

Equation of inverse variation:-

`y=(k)/(x)`, where k is variation constant.

Given : The time it takes to remodel a kitchen t(p) varies inversely with the number of workers assigned to the job p.

i.e.
`t(p)=(k)/(p)` (1)

A kitchen remodeling job takes 40 hours to complete when 2 workers are assigned to it.

i.e.
`t(2)=40=(k)/(2)`

`\Rightarrow k=40*2=80`

Then , the equation can be used to find the time to complete the job when p workers are assigned to it (Put k= 80 in (1)) :

`t(p)=(80)/(p)`