# If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

#### Answer:

2.4\ \text{hrs

#### Explanation:

Sally alone can paint a house in $4 \setminus \textrm{h r s}$ Hence (fraction of) the work done by Sally in one hour

$= \frac{1}{4}$

Now, John alone can paint the house in $6 \setminus \textrm{h r s}$ Hence (fraction of) the work done by John in one hour

$= \frac{1}{6}$

If it takes $x \setminus \setminus \textrm{h r s}$ for Sally & John to paint the same house working together then the work done Sally & John in $x$ hrs will be (complete) $1$

$\setminus \therefore x \left(\frac{1}{4} + \frac{1}{6}\right) = 1$

$x \left(\frac{5}{12}\right) = 1$

$x = \frac{12}{5}$

$x = 2.4$

Therefore it takes 2.4\ \text{hrs for Sally & John to paint the house together