SOLUTION: Beth can paint a room in 8 hours. She begins and is joined 3 hrs later by Aaron. The two of them complete the job in 2.5 more hours. How long would it take Aaron to paint the room

Question 1032871: Beth can paint a room in 8 hours. She begins and is joined 3 hrs later by Aaron. The two of them complete the job in 2.5 more hours. How long would it take Aaron to paint the room alone?
Found 4 solutions by stanbon, josgarithmetic, MathTherapy, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Beth can paint a room in 8 hours. She begins and is joined 3 hrs later by Aaron. The two of them complete the job in 2.5 more hours. How long would it take Aaron to paint the room alone?
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Beth rate: 1/8 job/hr
In 3 hrs Beth does 3/8 of the job.
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Aaron's rate is 1/x job/hr
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2.5(1/8 + 1/x) = 5/8 job
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(1/8 + 1/x) = 1/4
(x+8)/(8x) = 1/4
x+8 = 8x
7x = 8
x = 8/7 hr = 1 hr 8 min 34 seconds (time for Aaron to do the job alone)
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Cheers,
Stan H.
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Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
"Paint the room" is one whole job. Beth and then Beth & Aaron do their work to complete 1 job. The rule can be stated RT=J to relate rate, time, amount of job.

Do you understand this equation? Observe and consider the two expressions on the left and that their sum is 1 whole job.
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

Beth can paint a room in 8 hours. She begins and is joined 3 hrs later by Aaron. The two of them complete the job in 2.5 more hours. How long would it take Aaron to paint the room alone?

Aaron takes:
Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.
A wide variety of similar introductory joint-work problems were solved for you with detailed explanations in these lessons

    - Using Fractions to solve word problems on joint work,
    - Solving more complicated word problems on joint work,
    - Selected joint-work word problems from the archive

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