Betty paint twice as fast as Dan. when working together Betty and Dan can paint 2400 square feet in 4 hours,another employee,sue joined their painting team.working together Dan,Betty and Sue can paint 36000 square feet in 3 hours.
if sue works alone,how many square feet can she paint in 4 hours and 27 minutes?
Let's determine the individual painting rates of Betty and Dan first.
Let B be the painting rate of Betty (in square feet per hour) and D be the painting rate of Dan (in square feet per hour).
Since Betty paints twice as fast as Dan, we have the following equation:
B = 2D
We know that when working together, Betty and Dan can paint 2400 square feet in 4 hours. Using their painting rates, we can set up the following equation:
4(B + D) = 2400
Simplifying the equation:
4B + 4D = 2400
Now, let's solve the equation for B and D:
B + D = 600 (Equation 1)
We also know that when working together with Sue, they can paint 36000 square feet in 3 hours. Using their painting rates, we can set up the following equation:
3(B + D + S) = 36000
Simplifying the equation:
B + D + S = 12000 (Equation 2)
To find Sue's painting rate, we need to express it in terms of Betty's rate:
S = 12000 - (B + D) (Substituting Equation 1 into Equation 2)
Now, let's substitute the expression for Sue's rate into Equation 1 and solve for the combined rate of Betty and Dan:
B + D + (12000 - (B + D)) = 600
12000 = 600
12000 = 2(B + D)
6000 = B + D
We now have the combined painting rate of Betty and Dan: B + D = 6000 (Equation 3)
To find the individual rates of Betty and Dan, we can use Equation 1:
B = 600 - D
Substituting this into Equation 3:
(600 - D) + D = 6000
600 = 6000
Therefore, Dan's individual painting rate is D = 600 feet per hour. Since Betty paints twice as fast as Dan, her individual painting rate is B = 2D = 2*600 = 1200 feet per hour.
Now, let's determine how many square feet Sue can paint in 4 hours and 27 minutes (or 4.45 hours). Since Sue joined the team, the combined rate of all three of them is 6000 square feet per hour (from Equation 3). Thus, in 4.45 hours, Sue can paint:
Sue's painting rate * Time = 6000 * 4.45 = 26700 square feet
Therefore, Sue can paint 26700 square feet in 4 hours and 27 minutes.
To find out how many square feet Sue can paint in 4 hours and 27 minutes, we'll need to use the information given in the problem.
First, let's determine the combined work rate of Dan and Betty. We know that Betty paints twice as fast as Dan, so their work ratio is 2:1.
In 4 hours, the two of them can paint 2400 square feet. To find their combined work rate per hour, we divide the total work completed by the number of hours:
Work rate of Dan and Betty = 2400 square feet / 4 hours = 600 square feet per hour.
Next, we are given that when Dan, Betty, and Sue work together, they can paint 36000 square feet in 3 hours. To find their combined work rate per hour, we divide the total work completed by the number of hours:
Work rate of Dan, Betty, and Sue = 36000 square feet / 3 hours = 12000 square feet per hour.
Now, we can determine Sue's work rate by subtracting the combined work rate of Dan and Betty from the work rate of all three of them:
Sue's work rate = Work rate of Dan, Betty, and Sue - Work rate of Dan and Betty
= 12000 square feet per hour - 600 square feet per hour
= 11400 square feet per hour.
To find out how many square feet Sue can paint in 4 hours and 27 minutes, we first convert 4 hours and 27 minutes to hours by dividing the minutes by 60:
4 hours and 27 minutes = 4 + (27/60) = 4.45 hours.
Finally, we can calculate the number of square feet Sue can paint in 4 hours and 27 minutes by multiplying her work rate by the time spent working:
Square feet painted by Sue = Sue's work rate * Time spent working
= 11400 square feet per hour * 4.45 hours
= 50730 square feet.
Therefore, Sue can paint 50730 square feet in 4 hours and 27 minutes.
We want their rate of painting in ft^2/hr. Thus
b = 2d
d + b = 2400/4
d + b + s = 3600/3
Solve for s, and then find
s * 4.45