This means Alice can paint 1/5 of the house in one hour, and Bob can paint 1/7 of the house in one hour, right? This brings us to the following equation:

Letxbe the work done in a hour by both of them:

1/5 + 1/7 = x

7/35 + 5/35 =12/35

That meansin a hour, they can do12/35of the house.

Which means, the entire work can be done in35/12hours (since the amount done in a hour multiplied by the number of hours should give1or if you prefer ).

35/12=2.916hours or 2 hours and 55 minutes rounded.

Voilà.