If 5 people can paint a house in 4 hrs, how long will it take 3 people??
As per book answer is 6 hrs 40 mints
But how????
So it would take 20 man-hours to paint the house, (or "person-hours to be politically correct)
No distribute those 20 hours needed among 3 painters, so it would take
20/3 hours
= 6 2/3 hours
= 6 hours and 40 minutes
To determine how long it will take 3 people to paint the house, we can use the concept of man-hours. Man-hours refer to the number of hours worked by a single person. In this scenario, we know that 5 people can paint the house in 4 hours.
First, we need to calculate the total man-hours required to paint the house. We can do this by multiplying the number of people by the number of hours: 5 people * 4 hours = 20 man-hours.
Now, we need to determine how long it will take 3 people to complete the same amount of work. To do this, we divide the total man-hours required (20) by the number of people (3): 20 man-hours / 3 people ≈ 6.67 man-hours.
Since we can't have partial man-hours, we round up to the nearest whole number. Therefore, it will take 3 people approximately 7 hours to paint the house.
However, the book answer you mentioned is 6 hours and 40 minutes, which is equivalent to 6.67 hours. So, it seems that the book rounded to the nearest 10 minutes instead of rounding up to the nearest hour.
To determine how long it will take 3 people to paint the house, you can use the concept of work.
The number of people and the time it takes to complete a task are inversely proportional, which means that as the number of people decreases, the time it takes to complete the task increases, and vice versa.
In this case, we can set up a proportion to solve the problem. Since 5 people can paint the house in 4 hours, that means the amount of work required to paint the house is the same.
Let's say the work required to paint the house is represented by W. Then, with 5 people, the work rate per hour would be W/4 (4 hours).
To find out how long it would take 3 people to do the same amount of work, we can set up the proportion as follows:
5 people / 3 people = 4 hours / x hours
Where x represents the time it takes for 3 people to complete the task.
By cross-multiplying and solving for x, we get:
5 * x = 3 * 4
5x = 12
x = 12 / 5
x = 2.4 hours
So, it would take 3 people approximately 2.4 hours to paint the house. To convert this into hours and minutes, we can multiply the decimal part (0.4) by 60 since there are 60 minutes in an hour:
0.4 * 60 = 24 minutes
Therefore, it would take 3 people approximately 2 hours and 24 minutes to paint the house, which is equivalent to 2 hours and 40 minutes.