SOLUTION: It would take Maricar 10 hours working alone to clean all hotel rooms, while it would take Marivic only 8 hours. How long would it take them to do the job together?

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Question 551677: It would take Maricar 10 hours working alone to clean all hotel rooms, while it would take Marivic only 8 hours. How long would it take them to do the job together?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
It would take Maricar 10 hours working alone to clean all hotel rooms, while it would take Marivic only 8 hours. How long would it take them to do the job together?
Let the desired time be x

Make this chart and put x for the time required working together, and 10 and
8 for the times for them working separately.

                        Number of        Number of          Rate in
                       jobs done       hours required      jobs/hour
Maricar working alone                        10 

Marivic working alone                         8

Both working together                         x


In all three cases 1 job is being done, so we fill in 1 for the number
of jobs:

                        Number of        Number of          Rate in
                       jobs done       hours required      jobs/hour
Maricar working alone      1                 10 

Marivic working alone      1                  8

Both working together      1                  x


Fill in the rates in jobs/hour by dividing jobs done by hours:


                        Number of        Number of          Rate in
                       jobs done       hours required      jobs/hour
Maricar working alone      1                 10              1%2F10 
Marivic working alone      1                  8              1%2F8 
Both working together      1                  x              1%2Fx

           The equation comes from

                 %28matrix%284%2C1%2C%22Maricar%27s%22%2C+rate%2Cworking%2Calone%29%29 + %28matrix%284%2C1%2C%22Marivic%27s%22%2C+rate%2Cworking%2Calone%29%29 = %28matrix%285%2C1%2Crate%2C+of%2Cboth%2Cworking%2Ctogether%29%29
 
                              1%2F10 + 1%2F8 = 1%2Fx

Solve that equation and get 40%2F9 or 4%264%2F9 hours or

4 hours, 26 minutes and 40 seconds.

Edwin