how long does it take.

Question

Linda and Kathy can clean a house in 5.14 hours together.  Working alone, it would of taken Linda 11 hours.  How long would it take Kathy to clean alone?

Answer 1

Let Lrate = Linda's cleaning job rate, job/hr

     Krate = Kathy's cleaning job rate, job/hr

 

To represent both girls cleaning together:

 

(Lrate + Krate)*t = 1        ( '1' represents house cleaning job)

 

t = 5.14 hr

Lrate = 1/11  job/hr

 

Krate = 1/t - Lrate = 1/5.14 hr - 1/11 hr = 0.10364 job/hr

 

Time to clean alone for Kathy;

 

Krate*t = 1     

 

t = 1/Krate = 1 job/0.10364 job/hr  = 9.65 hr     it would take Kathy to clean the house alone