Question

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 1

`2.4\ \text{hrs`

Explanation:

Sally alone can paint a house in `4\ text{hrs}` Hence (fraction of) the work done by Sally in one hour

`=1/4`

Now, John alone can paint the house in `6\ text{hrs}` Hence (fraction of) the work done by John in one hour

`=1/6`

If it takes `x\ \text{hrs}` for Sally & John to paint the same house working together then the work done Sally & John in `x` hrs will be (complete) `1`

`\therefore x(1/4+1/6)=1`

`x(5/12)=1`

`x=12/5`

`x=2.4`

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