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?
<pre>
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              {{{1/10}}} 
Marivic working alone      1                  8              {{{1/8}}} 
Both working together      1                  x              {{{1/x}}}

           The equation comes from

                 {{{(matrix(4,1,"Maricar's", rate,working,alone))}}} + {{{(matrix(4,1,"Marivic's", rate,working,alone))}}} = {{{(matrix(5,1,rate, of,both,working,together))}}}
 
                              {{{1/10}}} + {{{1/8}}} = {{{1/x}}}

Solve that equation and get {{{40/9}}} or {{{4&4/9}}} hours or

4 hours, 26 minutes and 40 seconds.

Edwin</pre>