Question

Jameer paints one wall of a house in 3 days. june paints two walls of a house in 5 days. if the two of them work together to paint a whole house that has 10 walls, how long will they take? (we assume that each wall takes the same amount of time to paint for any fixed individual.)

Answer 1

Let the number of days be x.

Jameer paints 1 wall in 3 days. In 1 day, he paints 1/3 of a wall. In x days, he paints (1/3)x walls.

June paints 2 walls in 5 days. In 1 day, she paints 2/5 of a wall. In x days, she paints (2/5)x walls.

Working together, in x days they paint (1/3)x + (2/5)x walls.

We want to know the number of days they will take to paint 10 walls, so we let the expression equal 10.

(1/3)x + (2/5)x = 10

(5/15)x + (6/15)x = 10

(11/15)x = 10

x = 10 * 15/11

x = 150/11

It will take 150/11 days which is the same as 13.6363... days or approximately 13.6 days.