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

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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) About Me  (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
:
80%2Fx + 80%2F%282x%29 + 80%2F%28%282x-120%29%29 = 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