Sally can paint a room in 9 hours while it takes Steve 6 hours to paint the same room. How long would it take them to paint the room if they worked together?

18/5 hours per room (3.6 hours per room)

Step-by-step explanation:

Sally's rate of work is 1 room in 9 hours = 1/9 room per hour

Steve's rate of work is 1 room in 6 hours = 1/6 room per hour

Their combined rate of work

= 1/9 + 1/6

= 2/18 + 3/18

= 5/18 room per hour.

we take the reciprocal of this to get their rate in hours per room

= (5/18)⁻¹

= 18/5 hours per room (3.6 hours per room)

5+2x=a

asdasdsaadsaddsasds

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4