Question 837171
Job completion as a uniform rates situation could be sorted using rate, time, job; in the same way as travel situations of rate, time, distance.  


The rate is as unit of "tanks emptied per hour", time is hours, and the job identified is, "emptying the tank".  The unknown time during which the second pipe operates is t.


Pipe ID__________rate___________time____________job
firstpipe________1/8____________2+t____________
secondpipe_______1/6____________t______________


Find expressions for the contributed amount of job of each pipe:


Pipe ID__________rate___________time____________job
firstpipe________1/8____________2+t____________(1/8)(2+t)
secondpipe_______1/6____________t______________(1/6)t
TOTAL____________________________________________1


The needed equation is the sum of the amounts of the job that the pipes had done, and this sum is ONE WHOLE JOB, or 1.
EQUATION:  {{{highlight((t+2)/8+t/6=1)}}}
Solve for t.
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LCD is 24.
{{{3(t+2)+4t=24}}}
{{{3t+6+4t=24}}}
{{{7t=24-6}}}
{{{7t=18}}}
{{{highlight(t=18/7=1&4/7)}}} hours