SOLUTION: Together, Michelle, Sal, and kristen can clean and wax a car in 1 hr 20 min. To complete the job alone, Michelle needs twice the time that Sal needs and 2 hr more than kristen. How

Question 202778: Together, Michelle, Sal, and kristen can clean and wax a car in 1 hr 20 min. To complete the job alone, Michelle needs twice the time that Sal needs and 2 hr more than kristen. How long would it take each to clean and wax the car working alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Together, Michelle, Sal, and kristen can clean and wax a car in 1 hr 20 min.
To complete the job alone, Michelle needs twice the time that Sal needs
and 2 hr more than kristen.
How long would it take each to clean and wax the car working alone?
:
Use minutes for the time: 1 hr 20 min = 80 min; 2 hr = 120 min
:
let x = time required by Sal alone
then
2x = Michelle's time alone
and
(2x-120) = Kristen's time alone
:
let the completed job = 1
:
+ + = 1
Multiply equation by 2x(2x-120) to clear the denominators
80(2(2x-120) + 80(2x-120) + 80(2x) = 2x(2x-120)
:
320x - 19200 + 160x - 9600 + 160x = 4x^2 - 240x
:
320x + 160x + 160x - 19200 - 9600 = 4x^2 - 240x
:
640x - 28800 = 4x^2 - 240x
:
0 = 4x^2 - 240x - 640x + 28800
:
0 = 4x^2 - 880x + 28800
Simplify, divide by 4
x^2 - 220x + 7200 = 0
Factor:
(x - 40)(x - 180) = 0
Two solutions,
x = 40; does not make sense
therefore
x = 180 min, (3 hrs) is Sal's time alone
then
2*180 = 360 min, (6 hrs) is Michelle's time alone
and
360 - 120 = 240 min, (4 hrs) is Kristen time
;
;
Check solution using 1.33 hr working together
1.33/3 + 1.33/6 + 1.33/4
.44 + .22 + .33 = .99 ~ 1
RELATED QUESTIONS
sam can complete a job in 20 minutes working alone. if he joined by the twins jim and tim (answered by ankor@dixie-net.com)

Luke, Eddie, and Ryan can complete a job in 1 hours and 20 minutes if they work together. (answered by richwmiller)

Luke,Eddie, and Ryan can complete a job in 1 hour and 20 minutes if they work together.... (answered by alicealc,richwmiller)

if so can wash and wax a car in one hour and half can do the same job in 8 hours how long (answered by richwmiller,Vladdroid)

Nancy and Angelica share in cleaning the house as a part of their training at home.... (answered by bostonmathtutor)

Nancy and Angelica share in cleaning the house as a part of their training at home.... (answered by mananth)

can some help me figure this out? Together John, Tina and Chris together completes the (answered by scott8148)

Greg and Randy together can repair a car in 4 4/17 hours. Randy, working alone could do... (answered by josgarithmetic)

Please help me with this word problem. Working together, two people can clean an office... (answered by ankor@dixie-net.com)