Question 469708
Frank and Angie are making pizzas for their business. If Frank can produce all of the necessary pizzas on his own in 6 hours and Angie can do the same job in 4 hours, then what portion of the day’s pizzas can they make together in 1 hour? 
<pre> 
Make this chart:
 
                       No of         
                       jobs or
                       fraction    time      rate
                       of job       in        in
                       done        hours   jobs/hour   
Frank
Angie
Both together
 
Let x be the answer, the fraction of the job done by
both.  So put x for the fraction of a job done by
both together and 1 for the time in hours:
 
                       No of         
                       jobs or
                       fraction    time      rate
                       of job       in        in
                       done        hours   jobs/hour   
Frank
Angie
Both together             x          1


 
Frank can do 1 job in 6 hours, and Angie can do 
the same job in 4 hours. So we put 1 for the number of jobs
Frank can do and 6 for the number of hours, and similarly
we put 1 for the number of jobs Angie can do and 4 for the 
number of hours.

                       No of         
                       jobs or
                       fraction    time      rate
                       of job       in        in
                       done        hours   jobs/hour   
Frank                     1          6
Angie                     1          4
Both together             x          1

Next we fill in all three rates in jobs/hour by dividing
number of jobs (or fraction of a job) by hours.

                       No of         
                       jobs or
                       fraction    time      rate
                       of job       in        in
                       done        hours   jobs/hour   
Frank                     1          6       1/6
Angie                     1          4       1/4
Both together             x          1       x/1 


{{{(matrix(4,1,

"Frank's",
rate, 
working,
alone)) +
(matrix(4,1,

"Angie's",
rate, 
working,
alone)) =

(matrix(5,1,

"Their",
combined,
rate, 
working,
together)) }}}

{{{1/6 + 1/4 = x/1}}}

{{{1/6 + 1/4 = x}}}

Multiply through by 12

{{{2 + 3 = 12x}}}

{{{5 = 12x}}}

{{{5/12 = x}}}

So working together they can do {{{5/12}}}ths of the job in 1 hour.

Edwin</pre>