Question 203098: 3 girls, Laura, Tammy, and Jeri can wash the car, clean the pool, and mow the lawn in 1 hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would each girl take to do the job alone?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 3 girls, Laura, Tammy, and Jeri can wash the car, clean the pool,
and mow the lawn in 1 hour and 20 minutes.
If Jeri did all the work, she would take twice as long as Tammy and
2 hours longer than Laura.
How long would each girl take to do the job alone?
:
Use minutes for the time: 1 hr 20 min = 80 min; 2 hr = 120 min
:
let x = time required by Tammy alone
then
2x = Jeri's time alone
and
(2x-120) = Laura's time alone (2hrs less than Jeri)
:
let the completed job = 1 (includes all three tasks
:
 +  +  = 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 Tammy's time alone
then
2*180 = 360 min, (6 hrs) is Jeri's time alone
and
360 - 120 = 240 min, (4 hrs) is Laura's time
;
;
Check solution using 1.33 hr working together
1.33/3 + 1.33/6 + 1.33/4
.44 + .22 + .33 = .99 ~ 1
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