SOLUTION: One pipe can empty a tank in 8 hours and a second pipe can empty the same tank in 6 hours. If the first pope operated alone for two hours and then the second pipe is put into opera

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Question 837171: One pipe can empty a tank in 8 hours and a second pipe can empty the same tank in 6 hours. If the first pope operated alone for two hours and then the second pipe is put into operation, how many hours after the second pipe is opened will the tank be empty?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
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%28%28t%2B2%29%2F8%2Bt%2F6=1%29
Solve for t.
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LCD is 24.
3%28t%2B2%29%2B4t=24
3t%2B6%2B4t=24
7t=24-6
7t=18
highlight%28t=18%2F7=1%264%2F7%29 hours