SOLUTION: Hank can wash and wax the car in 2 hours, Sally can do it in 1 hour, 30 minutes, and Hank, Sally, and Lena can do it in 40 minutes working together. How long would it take Lena,

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hank can wash and wax the car in 2 hours, Sally can do it in 1 hour, 30 minutes, and Hank, Sally, and Lena can do it in 40 minutes working together. How long would it take Lena,       Log On

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Question 923126: Hank can wash and wax the car in 2 hours, Sally can do it in 1 hour, 30 minutes, and Hank, Sally, and Lena can
do it in 40 minutes working together. How long would it take Lena, working alone, to wash and wax the car?
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
Hank can wash and wax the car in 2 hours
so in 1 hr , he can do 1/2 of the work
Sally can do it in 1 hour, 30 minutes (1.e 1.5 hr)
so in 1 hr he can do 1/1.5 of the work
three persons together can do it in 40 min ( 40 min = 40/60 = 2/3 hr)
three persons together can complete in 2/3 hr
In 1 hr they can do 1%2F%282%2F3%29 work
= 3%2F2 work
I hr, lena alone can do = +3%2F2-+1%2F1.5+-+1%2F2 of the work
=3%2F2+-1%2F%283%2F2%29+-1%2F2 of the work
=+3%2F2-+2%2F3-1%2F2 of the work
multiply and divide with 6 to each term
= %283%2F2%29+%2A%286%2F6%29-+%282%2F3%29%2A%286%2F6%29-%281%2F2%29%2A%286%2F6%29 of the work
=%283%2F1%29+%2A%283%2F6%29-+%282%2F1%29%2A%282%2F6%29-%281%2F1%29%2A%283%2F6%29 of the work
=9%2F6-+4%2F6-3%2F6 of the work
= +%289-4-3%29%2F6 of the work
= 1%2F3 of the work
so , 1 Hr Lena can do 1/3 of the work
so to complete full work , lena can take 3 hrs
so result is 3 hrs