If Joe can paint a house in 15 hours and Sam can paint the same house in 10 hours, we can find their combined painting rate by adding their individual rates. The combined rate is 1/15 + 1/10 = 1/6.
To determine how long it takes them to paint the house together, we can take the reciprocal of their combined rate. So, it would take them 6 hours to paint the house together.