if sally can paint a house in 4 hours and john can paint the same house in 6 hours how long will it take for both of them to paint the house together?

Question

1. 2 hours and 24 minutes
2. 3 hours and 12 minutes
3. 3 hours and 44 minutes
4. 4 hours and 10 minutes or
5. 4 hours and 33 minutes 

Answer 1

Hi Aja,

 

Here's how you solve this.

 

If Sally can paint the house in 4 hours, in one hour she can paint 1/4 of the house.

If John can paint the house in 6 hours, in one hour he can paint 1/6 of the house.

 

To see how much of the house they can paint together in one hour, we add these together.

 

 1/4  +  1/6  = 1/x    

 

(1/x is how much of the house they can paint together in one hour.  Therefore x is the number of hours it will take them both to pain the house)

 

 

1/4 + 1/6 = 1/x

3/12 + 2/12 = 1/x        (Find Least Common Denominator)

5/12 = 1/x                   (Add the fractions)

5/12 x = 1                   (Multiply both sides by X)

X = 12/5 = 2.4 hours    (Divide both sides by 5/12)

 

Together it will take them 2hours and 24min to paint the house.

 

 

Hope this helps!

Emily