A group of students have volunteered for the student council car wash. Janet can wash a car in m minutes. Rodrigs can wash a car in m-5 minutes, while Nick needs the same amount of time as Janet.If they all work together, they can wash a car in about 3.23 minutes. How long does Janet take to wash a car?
pls help. I tried it couple of times but did not get the answer.
Let's assume that Janet takes m minutes to wash a car. According to the given information, Nick also takes m minutes to wash a car.
Rodrigs takes m - 5 minutes to wash a car.
When they all work together, they can wash a car in about 3.23 minutes.
Let's calculate the work rates of each person and combine them to find the total work rate when they all work together.
The work rate of Janet is 1 car per m minutes.
The work rate of Rodrigs is 1 car per (m - 5) minutes.
The work rate of Nick is also 1 car per m minutes.
Let's denote the work rate when they all work together as X car per minute.
So, the combined work rate equation is:
1/m + 1/(m - 5) + 1/m = X/3.23
To further solve this equation, we need to eliminate the fractions. Let's multiply every term by m(m - 5)(3.23):
m(m - 5)(3.23)(1/m) + m(m - 5)(3.23)(1/(m - 5)) + m(m - 5)(3.23)(1/m) = m(m - 5)(3.23)(X/3.23)
Canceling out common terms:
3.23(m - 5) + 3.23m + 3.23m = X(m - 5)m
To find the time it takes for Janet to wash a car, we can follow these steps:
Let's assume Janet takes x minutes to wash a car.
Given that Nick also takes the same amount of time as Janet, Nick also takes x minutes to wash a car.
Rodrigs, on the other hand, takes m-5 minutes to wash a car.
When they work together, their combined work rate is equal to the reciprocal of the time it takes them to complete the task.
So we can set up the equation:
1/x + 1/x + 1/(m-5) = 1/3.23
To simplify the equation, we need to find a common denominator.
The common denominator here is 3.23*x*(m-5), so we multiply each term by this denominator:
(3.23*x*(m-5)/x) + (3.23*x*(m-5)/x) + (3.23*x*(m-5)/(m-5)) = (3.23*x*(m-5)/3.23)
Cancelling out common factors:
3.23*(m-5) + 3.23*(m-5) + 3.23*x = x(m-5)
Expanding and simplifying:
6.46*(m-5) + 3.23*x = x*m - 5*x
6.46m - 32.3 + 3.23x = xm - 5x
6.46m - xm + 32.3 = 5x - 3.23x
Combining like terms:
(6.46m - xm) + 32.3 = (5 - 3.23)x
(6.46m - xm) + 32.3 = 1.77x
Rearranging the equation:
xm + 1.77x = 6.46m + 32.3
Factoring out x:
x(m + 1.77) = 6.46m + 32.3
Dividing both sides by (m + 1.77):
x = (6.46m + 32.3) / (m + 1.77)
Now you can substitute the values you have for m in the equation above and calculate the value of x, which is the time it takes for Janet to wash a car.
m+m+m-5=3.23
3m=8.23
m= 8.23/3