Question

The amount of time it takes p people to paint d doors varies directly with the number of doors and inversely with the number of people. Four people can paint 10 doors in 2 hours. How many people will it take to paint 25 doors in 5 hours?

4
5
10
20

Answer 1

it will take 2 people to paint 25 doors in 5 hours.

Answer 2

4 people

Explanation:

We are given that The amount of time it takes p people to paint d doors varies directly with the number of doors inversely with the number of people.

Let constant of proportionality be k

There are 4 people , 10 doors and 2 hours.

Since we are given that time varies directly with no. of doors and inversely with no. of people.

`2=k*(10)/(4)`

`(2*4)/(10)=k`

`(8)/(10)=k`

`(4)/(5)=k`

Now we are supposed to find that How many people will it take to paint 25 doors in 5 hours.

⇒
`5=k*(25)/(d)`

⇒
`5=(4)/(5) *(25)/(d)`

⇒
`d=(4)/(5) *(25)/(5)`

⇒
`d=4`

Hence it will take 4 people to paint 25 doors in 5 hours.