Question 713049
One job is filling the pool.  Rate as gallons per hours.
Rate*Time=Jobs


Pump__________rate__________time_____________jobs
A_____________1/30_____________30____________1
B______________r______________({{{t}}})____________1
A & B__________1/12______________12_____________1


While A and B work together, each pump contributes its own rate to the sum of the simultaneous rates.  


{{{highlight(1/30+r=1/12)}}}, find r, which is units of jobs per hour.  Note that the question is asking how many hours to fill the pool by pump B alone, which means how many hours per 1 job.  This is the RECIPROCAL of r.  We essentially are looking for {{{t}}} in the above table.


{{{r=1/12-1/30}}}
{{{r=(5-2)/30}}}
{{{r=3/30}}}, {{{highlight(r=1/10)}}}
Answer:  That means 10 hours for pump B to fill the pool