Question

Lyle can paint a room in 3 hours. Selena can paint a room with the same dimensions in 2 hours. If they work together, how many hours does it take them to paint the room? Round your answer to the nearest tenth.

Answer 1

ANSWER
1.2 hours

EXPLANATION 
Let x represent the number of hours it takes to complete the paint job.
The fraction of a job done per hour with both of them working is 1/x.

Lyle does 1/3 of the painting in one hour
(For example, if it took 3 hours to paint the room, then in one hour, only 1/3 of the room will be painted. In two hours, 1/3 + 1/3  = 2/3 of the room will be painted. In three hours, 1/3+1/3+1/3=3/3=1 of the room will be painted---completed)

Selena does 1/2 of the painting in one hour.

Therefore, for one hour, the fraction of the Job that Lyle does added with the fraction of the Job that Selena does is equal to 1/x, which is the fraction of the job done with both of them working

   1/3 + 1/2 = 1/x

Multiply both sides of the equation by x

   x/3 + x/2 = 1

Factor out x from the left side

   x(1/3 + 1/2) = 1

Combine fractions. Get a common denominator for 1/3 and 1/2.
LCD of 1/3 and 1/2 is 6. 1/3 is equivalent to 2/6 and 1/2 is equivalent to 3/6.

   x(2/6 + 3/6) = 1
   x (5/6) = 1
   x = 1 * 6/5
   x = 6/5
   x = 1.2 hours

ALTERNATIVE EXPLANTION:
   job = rate · time ⇔ rate = job/time ⇔ time = job/rate

Lyle can do 1 paintjob of the room in 3 hours. Therefore, Lyle's rate is 1/3 paintjob per hour.

Selena can do 1 paintjob of the room in 2 hours. Therefore, Selena's rate is 1/2 paintjob per hour.

Their rate when working together is combined:

   rate = 1/3 + 1/2 = 2/6 + 3/6 = 5/6

Since time = job/rate and we are interested in 1 paintjob, then job = 1 and

   time = 1 / (5/6) = 6/5 = 1.2 hours