Joe works at the rate of  1/6 house per hour

Same works at the rate of 1/8 house per hour



Together (assuming they work without interfering with each other in any way), they work at the rate of  1/6 + 1/8  = 4/24 + 3/24 = 7/24 house per hour.



To paint one house (1 = 24/24), they take  (24/24)/(7/24) = 24/7 hours or about 3.42 hours (3hr 25min 43sec).



You can qualitatively sanity check this answer as follows:  notice each can paint the house individually in roughly 7 hours. For that rate you'd expect 3.5 hrs working together.  The obtained answer of 3.42hrs is close to this value, as one would (should) expect.   

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
 If Joe can paint a house in 6 hours and Sam can paint

the same house in 8 hours how long does it take 

them to do in working together 

-----------------

Here's a "shortcut" usable for parallel work, parallel flows, parallel resistors, etc.

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

 how long does it take them to do in working together?

6*8/(6+8) = 48/14 = 24/7 hours 

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


Here is an alternative to the standard algebraic solution shown by one of the other tutors, and without using the shortcut shown by the other tutor.


Consider the least common multiple of the two given times, which is 24 hours.


In 24 hours, Joe could paint 24/6 = 4 of these houses; in 24 hours Sam could paint 24/8 = 3 of them.  So in 24 hours the two together could paint 4+3 = 7 houses.


That means the number of hours it would take the two of them to paint the one house is 24/7.


ANSWER: 24/7 hours


 

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