SOLUTION: It takes Sharon 36 hours to paint an apartment. Eva can paint the same apartment in 30 hours. Eva starts the painting alone and works for 12 hours. Then Eva and Sharon paint toget

Question 1145634: It takes Sharon 36 hours to paint an apartment. Eva can paint the same apartment in 30 hours. Eva starts the painting alone and works for 12 hours. Then Eva and Sharon paint together for 3 hours. When Eva leaves, Sharon completes the job working on her own. How long does it take Sharon to finish the job?
Found 2 solutions by VFBundy, MathTherapy:
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Sharon's rate of work = 1/36 job per hour
Eva's rate of work = 1/30 job per hour

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"Eva starts the painting alone and works for 12 hours."

Rate of work * Hours worked = Portion of job completed

1/30 * 12 = 12/30 = 2/5

Because Eva completed 2/5 of the job, this means 3/5 of the job remains.

=========================================

"Then Eva and Sharon paint together for 3 hours."

Eva's rate of work + Sharon's rate of work = 1/36 + 1/30 = 5/180 + 6/180 = 11/180

Rate of work * Hours worked = Portion of job completed

11/180 * 3 = 33/180 = 11/60

Before Eva and Sharon started working together, 3/5 of the job remained. Working together, Eva and Sharon completed 11/60 of the job. So, to find out how much of the job now remains, subtract 11/60 from 3/5:

3/5 - 11/60 = 36/60 - 11/60 = 25/60 = 5/12

At this point 5/12 of the job remains.

=========================================

"When Eva leaves, Sharon completes the job working on her own. How long does it take Sharon to finish the job?"

Because we are told Sharon will complete the job...and we know that 5/12 of the job remains...this means Sharon will complete 5/12 of the job.

Rate of work * Hours worked = Portion of job completed

1/36 * h = 5/12

Multiply each side of the equation by 36:

h = 36(5/12)

h = 180/12 = 15

It takes Sharon 15 hours to complete the job.
Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

It takes Sharon 36 hours to paint an apartment. Eva can paint the same apartment in 30 hours. Eva starts the painting alone and works for 12 hours. Then Eva and Sharon paint together for 3 hours. When Eva leaves, Sharon completes the job working on her own. How long does it take Sharon to finish the job?

Sharon can do the job in 36 hours, or
Eva can do the job in 30 hours, or
Time Eva worked, ALONE: 12 hours
Time BOTH worked: 3 hours
Time Sharon worked, ALONE: "T" hours
With the end result being 1 COMPLETE job, we get:
---- Simplifying above equation
72 + 15 + 18 + 5T = 180 ------- Multiplying by LCD, 180
5T = 180 - 105
5T = 75
T, or time Sharon takes to complete the job =
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