Sal can paint a room in 6 hours while it takes Steve 5 hours. How long would it take them to paint the room together?

Question

saifoo.khan · Answer

$$\frac{1}{6}+\frac{1}{5}=\frac{1}{x}$$

saifoo.khan · Answer

x = 30/11

anonymous · Answer

$$(\frac{1}{6}+\frac{1}{5})t=1$$

$$\frac{11}{30}t=1$$
$$t=\frac{30}{11}$$

anonymous · Answer

clear or not?

anonymous · Answer

i'm looking for a number of hours I think?

anonymous · Answer

trick is to make the job 1 for "one whole job"

anonymous · Answer

then just add the rates. one does 1/5 per hour, other does 1/6 per hour so combined they do 
$$\frac{1}{5}+\frac{1}{6}=\frac{11}{30}$$ per hour.  that is their combined rate

anonymous · Answer

you want the whole job done so set 
$$\frac{11}{30}t=1$$ where t is time and get 
$$t=\frac{30}{11}$$

anonymous · Answer

okay, okay... yes that is the right answer!! I was confused. thnx!!

anonymous · Answer

if you don't like the form of the answer you could write 
$$2\tfrac{8}{11}$$ hours

anonymous · Answer

yw