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?
:
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/x}}} + {{{80/(2x)}}} + {{{80/((2x-120))}}} = 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