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 peopleFour people can paint 10 doors in 2 hoursHow many people will it take to paint 25 doors in 5 hours?

4 people

Step-by-step explanation:

This problem is a compound rule of three problem. The variables are:

number of people, number of doors, amount of time

the amount of time increases if the number of doors decreases, but the amount of time decreases if the number of people increases.

We can solve this problem by parts (using two simple rule of three):

4 people can paint 10 doors in 2 hours

Let's first find how many people would take to paint 25 doors in 2 hours (we make the amount of hours constant, so the rule of three is between number of people and number of doors):

4 people - > 10 doors - > 2 hours

X people - > 25 doors - > 2 hours

4/X = 10/25

X = 25*4/10 = 100/10 = 10

It would take 10 people to paint 25 doors in 2 hours.

Now, we make a inverse rule of three between the number of people and amount of time:

10 people paint 25 doors in 2 hours, how many people paint 25 doors in 5 hours:

10 people - > 25 doors - > 2 hours

X people - > 25 doors - > 5 hours

10*2 = X*5

X = 20/5 = 4 people