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?

1 Answer

Answer:

#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