Question

Suppose 4 people can paint a house if they work 3 days each. How long would it take a crew of 5 people to paint the house?

Answer 1

how long did it take the crew of 4 people to paint the house?

Answer 2

Good question. Four people working together can paint the house in 3 days total.
Therefore, one person working alone could paint the house in how many days?
We need to come up with a rate: 1 person can paint (what fraction) of a house per day.
Think about that.

Answer 3

Units of measurement may be helpful. After thinking about this problem, I came to the conclusion that 1 person can paint 1/12 of the house in 1 day. Check that out. Does that seem correct/ If so, apply it to the case where we have a crew of 5 instead of 4 people.

Answer 4

Here's my reasoning at this point:
If 4 people can paint 1 house in 3 days,
1 person can paint 1 house in 12 days (I divided "4 people" in the previous statement by 4, and then, in compensation, did the opposite, or multiplied, 3 days by 4, obtaining 12 days.
1 person can paint 1 house in 12 days.
5 people can paint 1 house in (12/5) days. (Again, I multiplied first by 5 and then divided the number of days by 5).

Therefore: 5 people can paint 1 house in 12/5, or 2.4, days.

Answer 5

Yes, the house takes 12 people-days of effort. If five people work that is 12/5 = 2.4 days.

Answer 6

Your use of "people-days" as your unit of measurement is very helpful. Thanks.

Answer 7

Thought it might be clearer. Good.