SOLUTION: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Question 401228: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Found 3 solutions by Tatiana_Stebko, dmf30633, Alan3354:
Answer by Tatiana_Stebko(1326)   (Show Source):
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Sally can paint a house in 4 hours, so in 1 hour she paints part of the house
John can paint the same house in 6 hour, so in 1 hour he paints part of the house
If they work together T hours, then Sally will paint part of house and John part of house, together they paint / In this case they will paint all house, so

T=2 2/5 hour
T=2hours 24min Sally and John need for paint all house together

Answer by dmf30633(3)   (Show Source):
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If sally paints one house in 4 hours =1/4 and John can paint one in 6 hours = 1/6, how long would it take for both to paint one house. First lets add our workers together.
1/4 + 1/6
finding the lowest common multiple at 12 we then
3*(1/4) + 2*(1/6)
resulting in
3/12 + 2/12
or
5/12
so we now know together sally and john can paint 5 houses in 12 hours
to find out how long it takes to do one, we simply divide 12 by 5

_2.4_____
5/12
10
20
20
0

It would take 2.4 hours to paint the house together.

Answer by Alan3354(30993)   (Show Source):
You can put this solution on YOUR website!
Use the shortcut, same time
= product/sum
= 4*6/(4 + 6)
= 24/10
= 2.4 hours