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

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

Let the answer be x hours:

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

So in one hour she can paint 1/4th of a house

So in x hours she can paint x times 1/4th of a house, 
or x/4ths of a house

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

So in one hour he can paint 1/6 of a house

So in x hours he can paint x times 1/6th of a house,
or x/6ths of a house

Therefore the x/4ths of a house that Sally paints plus
the x/6ths of a house that John paints must equal
1 house painted, so

  x/4 + x/6 = 1

Solve that by multiplying thru all terms by LCD of 12

Answer = 2.4 hours or 2 hours 24 minutes.

Edwin