paul paints a house in 4 hours, mike paints the same house in 6 hours. how long will it take them both to paints this house?
paul's rate = house/4
Mike's rate = house/6
combined rate = house/4 + house/6
= 5(house)/12
time for both = house/(5house/12)
= 12/5 = 2.4 hours
To find out how long it will take Paul and Mike to paint the house together, we need to calculate the rate at which they each paint. We can do this by finding the inverse of each person's painting time.
Paul's painting rate is 1 house per 4 hours, which means he paints at a rate of 1/4 house per hour.
Mike's painting rate is 1 house per 6 hours, which means he paints at a rate of 1/6 house per hour.
To find out how long it will take them both to paint the house together, we'll add their rates:
1/4 + 1/6 = 3/12 + 2/12 = 5/12
The combined rate of Paul and Mike is 5/12 house per hour. To find out how long it will take them to paint the house together, we can take the reciprocal of this fraction:
12/5 hours
Therefore, it will take Paul and Mike approximately 12/5 hours, or 2.4 hours, to paint the house together.