A new development has 105 houses, all same size. if Evan can paint a house in 4 days and Joel can paint a house in 3 days, how many weeks will it take them working together to paint all 105? A normal work week is 5 days.
How much of a house can they paint in a day?
1/4 + 1/3 = 7/12
So, at 7/12 house per day
105 / (7/12) = 180 days = 36 weeks
To find out how many weeks it will take Evan and Joel to paint all 105 houses, we need to calculate their combined painting rate and then divide the total number of houses by that rate.
First, let's find the individual painting rates of Evan and Joel. Evan can paint a house in 4 days, so his painting rate is 1 house per 4 days, or 1/4 houses per day. Similarly, Joel can paint a house in 3 days, so his painting rate is 1 house per 3 days, or 1/3 houses per day.
To find their combined painting rate, we'll add up their individual rates: 1/4 + 1/3 = 3/12 + 4/12 = 7/12 houses per day.
Now, we need to find how many days it will take them to paint 105 houses together. We can do this by dividing the total number of houses by their combined painting rate: 105 / (7/12) = 105 * (12/7) = 180 days.
Since a normal work week consists of 5 days, we can divide the total number of days by 5 to find the number of weeks it will take: 180 / 5 = <<180/5=36>>36 weeks.
Therefore, it will take Evan and Joel working together approximately 36 weeks to paint all 105 houses.