# Math

posted by on .

If sally can paint a house in 4 hours and John can paint the same house in 6 hours. How long will it take for them to paint the house together?

• Math - ,

HINT

Sally can paint 3 houses in 12 hours.
John can paint 2 houses in 12 hours.

Therefore, Sally and John together can paint 5 houses in 12 hours.

So, at the same rate, how long will it take them to paint 1 house together?

• Math - ,

Would you please further explain? I'm lost.

• Math - ,

Use Leo's hint that together they could paint 5 houses in 12 hours.

Divide: 12 by 5 = 2.4

That means that Sally and John together can paint a house in 2.4 hours.

• Math - ,

or..

Sally's rate = house/4 hrs
John's rate = house/6 hours

combined rate = house/4 + house/6 = 5house/12

so time with combined rate = house/(5house/12) = 12/5 = 2.4 hours

• Math - ,

How did you come up with the combine rate of house/4 + house/6 = 5houses/12?

• Math - ,

house/4 + house/6
= house(1/4 + 1/6)
= house(5/12)
= 5house/12

house is just my name for the constant, you could call it anything you want, say x or y or a or b ....

in the end it cancels

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