six people can paint a house in 3 days, how long it would take two people to paint it? I should show steps. It is related to rte of work.
First decide if
"six people can paint a house in 3 days"
is a direct proportion.
Since more people will paint in less days, it is not a direct proportion.
It is easier if we convert it to a direct proportion by saying:
"six people can paint 1/3 of a house each day"
so:
6 people : 1/3 of a house per day
1 person : 1/18th of a house per day.
2 people : 1/9th of a house per day,
so it takes 2 people 9 days to paint a house.
If 6 people paint a house in 3 days it will take 2 people (6/2)3 = 9 days to paint the house.
To find out how long it would take two people to paint the house, we need to understand the concept of rate of work. The rate of work is the amount of work done per unit of time. In this case, we can assume that the amount of work required to paint the house is the same.
Given that six people can paint the house in 3 days, we can determine their collective rate of work.
Let's say the rate of work for six people is represented by R. So, the work completed by the six people in one day would be 1/3 of the total work.
The rate of work for each person can be calculated by dividing the collective rate of work (R) by the number of people (6):
Rate of work per person = R/6
Now we need to determine the rate of work for two people.
Rate of work for two people = (R/6) * 2
This is because there are only two people working in this scenario.
To find the time it would take for two people to complete the work, we can use the equation:
Time = Work / Rate of work
Given that the amount of work is 1 (since the house is being completely painted), and the rate of work for two people is (R/6) * 2, we can substitute these values into the equation to solve for time:
Time = 1 / ((R/6) * 2)
Simplifying further:
Time = 1 / (R/3)
Therefore, it would take two people (assuming the same rate of work) 3 days to paint the house.
To summarize:
1. Find the collective rate of work for six people over three days.
2. Calculate the rate of work per person by dividing the collective rate of work by the number of people.
3. Multiply the rate of work per person by the number of people in the new scenario (two people) to find their rate of work.
4. Use the equation Time = 1 / (Rate of work) to find the time it would take two people to paint the house, given the rate of work.
5. Simplify the equation to obtain the final answer.