SOLUTION: If Sara 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 working together to paint the same house.

If Sara 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 working together to paint the

same house.

'

Let x = the number of hours it will take both of them working together.

`

>>...Sara can paint a house in 4 hours...<<

`

Translation: In one hour she can paint 1/4th of the house, so

in x hours she can paint x/4ths of the house.  That is to say, the fraction of

the house that she paints in those x-hours is x/4.

`

>>...John can paint the same house in 6 hours...<<

`

Translation: In one hour she can paint 1/6th of the house, so

in x hours she can paint x/6ths of the house. That is to say, the fraction of

the house that he paints in those x-hours is x/6.

`

The fraction of the house that Sara paints +

`     the part of the house that John paints =

`          1 house

` ` ` ` ` ` ` ` ` ` ` ` `x/4 + x/6 = 1

Multiply thru by LCD = 12 to clear of fractions

` ` ` ` ` ` ` ` ` `12·x/4 + 12·x/6 = 12·1

` ` ` ` ` ` ` ` ` ` ` ` ` `3x + 2x = 12

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 5x = 12

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `x = 12/5 = 2 2/5 hours or 2 hours 24 minutes

Edwin