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

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Question 249668: If Sally can paint a house in a 4 hours, and John can paint the same house in 6 hours, How long will it take for both of them to paint the house together?
Found 3 solutions by richwmiller, Alan3354, Edwin McCravy:
Answer by richwmiller(17219)   (Show Source):
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What is this a doll house?
You can't paint a house in 4 hours. There is preparation, sanding, masking, trim.
in one hour Sally paints 1/4 of the house
in one hour John paints 1/6 of the house
add up john's time and sally time together is equal to one

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
If Sally can paint a house in a 4 hours, and John can paint the same house in 6 hours, How long will it take for both of them to paint the house together?
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Use product/sum
= 4*6/(4+6) = 24/10
= 2.4 hours.
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The long way:
S does 1/4 of the house per hour.
J does 1/6 per hour.
Together, they do 1/4 + 1/6 per hour = 5/12
5/12 house per hour --> 12/5 hours per house
= 2.4 hours.

Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website!
if one painter can paint a house in 6 hours, and another painter paints a house in 9 hours. How long will it take them to paint the house working together
If Sally can paint a house in a 4 hours, and John can paint the same house in 6 hours, How long will it take for both of them to paint the house together?

Let x = the number of hours working together (what is asked for) Make this chart: No. of Houses Rate Time Sally John ------------------------------------------------------ both together Fill in x for the time for both together to paint 1 house: No. of Houses Rate Time Sally John ------------------------------------------------------ both together 1 x

>>...Sally can paint a house in 4 hours...<<

So fill in 1 house and 4 hours for the Sally, her no. of houses and her number of hours, respectively. No. of Houses Rate Time Sally 1 4 John ------------------------------------------------------ both together 1 x

>>...John can paint the same house in 6 hours...<<

So fill in 1 house and 9 hours for John, his no. of houses and his number of hours, respectively. No. of Houses Rate Time Sally 1 4 John 1 6 ------------------------------------------------------ both together 1 x Now fill in all three rates using the formula No. of Houses Rate Time Sally 1 1/4 4 John 1 1/6 6 ------------------------------------------------------ both together 1 1/x x Now form the equation by using the fact that Sally's rate + John's rate = their rate together Can you get a LCD of 12x and solve that equation for x? If not post again asking how to. Answer: hours or hours or hours or hours and minutes. Edwin