If Sally can paint a house in 4 hours, & John can paint the same house in 6 hours, how long will it take for both of them to paint the house together? '
I am having trouble remembering how to set up the equation?
Amount of work accomplished =
(Rate of work) x time
The rates of work are measured in houses per hour, and can be added for the two workers. Sally's rate is 1/4 house per hour. John's rate is 1/6 house per hour.
1 house = (1/6 + 1/4)* Time
Time = 1/(1/6 + 1/4) = 1/(2/12 + 3/12)
= 1/(5/12) = 12/5 hour = 2 2/5 hr
That is two hours and 24 minutes
4 x 6 = 24
4 + 6 = 10
24/10 = 2.4 hours
To set up the equation, you need to consider the rate at which Sally and John can paint houses. The rate of work is measured in houses per hour.
Let's start by finding Sally's and John's rates.
Sally can paint a house in 4 hours, so her rate of work is 1 house per 4 hours, or 1/4 house per hour.
John can paint the same house in 6 hours, so his rate of work is 1 house per 6 hours, or 1/6 house per hour.
To find how long it will take for both of them to paint the house together, you need to add their rates of work. The combined rate is (1/4) + (1/6) = (3/12) + (2/12) = 5/12 house per hour.
Now, we can set up the equation to find the time it will take for both of them to paint the house together:
(amount of work) = (rate of work) x (time)
Since we want to find the time, we can rearrange the equation as:
time = amount of work / rate of work
In this case, the amount of work is 1 house, and the combined rate of work is 5/12 house per hour.
So, the equation becomes:
time = 1 / (5/12)
To divide by a fraction, you invert and multiply. So, the equation simplifies to:
time = 1 * (12/5)
Multiplying 1 by 12/5 gives us:
time = 12/5 hour
Since hours can be represented as a combination of hours and minutes, we can convert 12/5 hour to hours and minutes.
Dividing 12 by 5 gives us a quotient of 2 with a remainder of 2. So, the time it takes for both of them to paint the house together is 2 hours and 2/5 hour.
Finally, let's convert 2/5 hour to minutes. Since there are 60 minutes in an hour, we can multiply 2/5 by 60:
(2/5) * 60 = 24 minutes
Therefore, it will take Sally and John 2 hours and 24 minutes to paint the house together.