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?
Sally can paint 3 houses in 12 hours.
John can paint 2 houses in 12 hours.
Together they can paint 5 houses in 12 hours.
12/5 = 2.4 hours per house
Sally paints a house in four hrs or .25house per hour
John paints house in 6 hrs or one in .166hrs
If they worked together .25+.166= .416 house per hour or,
1/.416= 2.4 hrs per house
To find out how long it will take for Sally and John to paint the house together, you can use the concept of "work rate."
First, you need to calculate their individual work rates. Sally can paint the house in 4 hours, so her work rate is 1/4 of the house per hour. Similarly, John's work rate is 1/6 of the house per hour because he can paint it in 6 hours.
To find their combined work rate, you add their individual work rates together. In this case, Sally's work rate is 1/4 and John's work rate is 1/6. So, their combined work rate is 1/4 + 1/6.
To simplify this fraction, you need to find a common denominator, which in this case is 12. Multiply 1/4 by 3/3 (which is equivalent to 1) to get 3/12. Multiply 1/6 by 2/2 to get 2/12.
Now, you can add the fractions together, so 3/12 + 2/12 equals 5/12.
This means that together, Sally and John can paint 5/12 of the house per hour.
To find out how long it will take them to paint the entire house, you can divide 1 by their combined work rate of 5/12.
Dividing 1 by 5/12 is the same as multiplying 1 by the reciprocal of 5/12, which is 12/5.
Therefore, it will take Sally and John (together) 12/5 hours to paint the house. This can also be written as 2.4 hours or 2 hours and 24 minutes.