2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take..

2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes

I know the answer, but I don't understand how it is found so please show the work too. thanks

Sally does 1/4 of the work in 1 hour, and John does 1/6 in an hour. In x hours, Sally does x/4 of the work, and John does x/6 of the work.

x/4 + x/6 = 1 house in x hours
3x/12 + 2x/12 = 12/12
5x = 12
x = 12/5 = 2 2/5 hours

1/5th of an hour is 60/5 = 12 minutes, so 2/5ths is 24 minutes.

The answer is 2 hours and 24 minutes.

Hope that helped.

It takes Sally 4 hours, so she paints 1/4 of the house per hour.

John paints 1/6 of the house per hour.

Turn that into 12ths so you can compare and you get Sally painting 3/12 per hour, and John 2/12 per hour. So together they paint 5/12ths per hour.

That means it takes them 2 hours to paint 10/12ths of the house. Now you just have to figure out how long it takes them to paint the last 2/12ths. Since they do 5/12ths per hour, it takes 2/5ths of an hour to do 2/12ths of the house.

1/5th of an hour is 12 minutes. So 2/5ths is 24 minutes. Thus 2hrs and 24 min to paint the house.

every hour Sally can paint 1/4 of the house and John can paint 1/6

try and work it from there

I would just kick John out and have Sally do it. She's obviously better at it.