SOLUTION: Tom can paint a fence in 5 hours and Huck can paint the same fence in 6 hours. Tom starts painting the fence at 10 AM. He paints for an hour before Huck joins him at 11 AM. Then t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Tom can paint a fence in 5 hours and Huck can paint the same fence in 6 hours. Tom starts painting the fence at 10 AM. He paints for an hour before Huck joins him at 11 AM. Then t      Log On


   

Question 1192759: Tom can paint a fence in 5 hours and Huck can paint the same fence in 6 hours. Tom starts painting the fence at 10 AM. He paints for an hour before Huck joins him at 11 AM. Then they work together to finish painting the fence. At what time will they finish painting the fence?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
PERSON        RATE                TIME QUANTITY

Tom           1%2F5                   1

Huck          1%2F6               

combined      1%2F5%2B1%2F6             cross%28x%2B1%29 x

The amount of work was 1 fence.

cross%28%281%2F5%29%2A1%2B%281%2F5%2B1%2F6%29%28x%2B1%29=1%29
%281%2F5%29%2A1%2B%281%2F5%2B1%2F6%29%2Ax=1
LCD is 5*6=30, so multiplying both sides by 30 can clear the denominators.
6%2B%286%2B5%29x=30
6%2B11x=30
11x=24
highlight%28x=24%2F11=2%262%2F11%29
about 2 hours 11 minutes----------you can figure out "what time" from this value.

Answer by ikleyn(52770) About Me  (Show Source):
You can put this solution on YOUR website!
.
Tom can paint a fence in 5 hours and Huck can paint the same fence in 6 hours.
Tom starts painting the fence at 10 AM. He paints for an hour before Huck joins him at 11 AM.
Then they work together to finish painting the fence. At what time will they finish painting the fence?
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            You are at serious danger,  since you have  INCORRECT  SOLUTION  from @josgarithmetic.

            I came to get rid you of this danger:  I brought a correct solution to you. 


Working during 1 hour, Tom made 1/5 of the job; 4/5 of the job remained.


The combined rate of work of two boys is  1%2F5+%2B+1%2F6 = 6%2F30+%2B+5%2F30 = 11%2F30.


Working with the combined rate of work  11%2F30, two boys need  

    %28%284%2F5%29%29%2F%28%2811%2F30%29%29 = %284%2A30%29%2F%285%2A11%29 = %284%2A6%29%2F11 = 24%2F11 = 2 2%2F11  hours,

    or about 2 hours and 11 minutes to complete the job.


So the job will be completed at about  11:00 am + 2 hours and 11 minutes, i.e. at about 1:11 pm.    ANSWER

Solved.

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Ignore the post by @josgarithmetic for the sake of your safety,
since it is hopelessly wrong.