Question 1208959
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You have the correct set up. 
To solve you can multiply everything by the LCD 30A and you should get 3A+30 = 5A. 
Which at this point should be fairly easy to solve.
The result is <font color=red>A = 15</font>.


Another option is to solve like so
{{{1/10+1/A = 1/6}}}


{{{A/(10A)+10/(10A) = 1/6}}} Rewrite each fraction in terms of a common denominator


{{{(A+10)/(10A) = 1/6}}}


{{{6(A+10) = 10A}}} Cross multiply


I'll let the student take over from here. 


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Another approach.


Let's say the job is to paint 600 square feet of wall and ceiling area. 
I arrived at this number by multiplying the given values 10 and 6. 
Then tacking on a 0 at the end to make the area a bit more realistic.


This number isn't particularly important since it can be changed to anything else. You will get the same result at the end.
Also, the "four rooms" can be changed to any number of rooms to get the same answer. So we'll ignore this figure.


Patrice can paint all 600 sq ft in 10 hours when working alone.
His rate is 600/10 = 60 sq ft per hour.
rate = amountDone/time


When Patrice and April work together, assuming neither person hinders the other, they paint all 600 sq ft in 6 hours.
rate = 600/6 = 100 sq ft per hour.


April's unit rate must be 100-60 = 40 sq ft per hour since the two people's individual rates add to the combined rate 100 sq ft per hour.


Let's see how long it takes her to do the job by herself.
rate*time = amountDone
time = amountDone/rate
time = (600 sq ft)/(40 sq ft per hr)
time = (600/40) hours
time = <font color=red>15 hours</font>
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