SOLUTION: Could you help me about this ? : Ben can paint a house in 36 hours. Carlos can pint the same house in 24 hours. They started working together but after 12 hours Ben quit. How much

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Could you help me about this ? : Ben can paint a house in 36 hours. Carlos can pint the same house in 24 hours. They started working together but after 12 hours Ben quit. How much      Log On


   

Question 202013: Could you help me about this ? :
Ben can paint a house in 36 hours. Carlos can pint the same house in 24 hours. They started working together but after 12 hours Ben quit. How much time was necessary for Carlos to finish the job alone?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's first find the hourly rate of each painter:
If Ben can paint the entire house in 36 hours, then he can paint 1%2F36 of the house in 1 hour.
If Carlos can paint the entire house in 24 hours, then he can paint 1%2F24 of the house in 1 hour.
Working together, Ben & Carlos can paint %281%2F36%29%2B%281%2F24%29+=+5%2F72 of the house in 1 hour.
In 12 hours they can paint %2812%29%2A%285%2F72%29+=+5%2F6 of the house, which leaves only 1%2F6 of the house to finish.
Now the question, how long will it take Carlos to finish the house?
Well, Carlos can do 1%2F24 in 1 hour, so you can let x = the number of hours Carlos needs and form a proportion:
1%2F6+=+x%2F24 Multiply the first fraction by 4%2F4 to get the common denominator of 24.
%284%2F4%29%2A%281%2F6%29+=+x%2F24 Evaluate.
4%2F24+=+x%2F24 so...
x+=+4
Carlos needs 4 hours to finish the job.