Question 325451
I'm afraid it's not that simple.


If "Sally can paint a room in 4 hours", then she can paint {{{1/4}}} of the room in 1 hour (divide each number by 4). So Sally's rate is {{{1/4}}} of a room per hour. Likewise, since "Joe can paint a room in 6 hours", he can paint {{{1/6}}} of the room in one hour. So his rate is {{{1/6}}} of a room per hour.



Now add the two rates to get: {{{1/4+1/6=3/12+2/12=5/12}}}



So their combined rate (if conditions are perfect) is {{{5/12}}} rooms per hour. In other words, together they can paint {{{5/12}}} of the room in one hour.



Now let 't' be the time that it takes them to complete the task. If we multiply the rate {{{5/12}}} by the time 't', we will get a complete job. This is simply denoted by 1 (since we want to paint <u>one</u> room).



Basically, we then get the equation {{{(5/12)t=1}}}



{{{(5/12)t=1}}} Start with the given equation.



{{{cross(12)(5/cross(12))t=1*12}}} Multiply both sides by 12.



{{{5t=12}}} Multiply and simplify



{{{(cross(5)t)/cross(5)=12/5}}} Divide both sides by 5.



{{{t=12/5}}} Simplify



So working together, they can paint 1 room in {{{t=12/5}}} hours. Convert it to a mixed fraction to get {{{12/5=2&2/5}}}. Finally, multiply {{{2/5}}} by 60 (to convert it into minutes) to get {{{60(2/5)=120/5=24}}}. So {{{12/5}}} or {{{2&2/5}}} hours is 2 hours and 24 minutes.



So they can paint the room in 2 hours and 24 minutes.