SOLUTION: Pipe A can fill a tank in 12 hours and pipe B can empty the tank in 18 hours.Both pipes are opened at 6 am & after some time pipe B is closed,&the tank is full at 8 pm on the same

Algebra ->  Equations -> SOLUTION: Pipe A can fill a tank in 12 hours and pipe B can empty the tank in 18 hours.Both pipes are opened at 6 am & after some time pipe B is closed,&the tank is full at 8 pm on the same       Log On


   

Question 825011: Pipe A can fill a tank in 12 hours and pipe B can empty the tank in 18 hours.Both pipes are opened at 6 am & after some time pipe B is closed,&the tank is full at 8 pm on the same day.At what time was the pipe B closed?
A)8 am
B)9 am
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
The time between 6am and 8pm is made of two time periods, x and y. One combination of pipes was used for x amount of time, and another combination of pipes was used for y amount of time.

Sum of the time periods was 14 hours. That is the amount of time from 6am to 8pm. We have our very important first equation:
highlight%28x%2By=14%29

The filling rate when both pipes A and B are open is 1%2F12-1%2F18=%283-2%29%2F%282%2A2%2A3%2A3%29=highlight_green%281%2F36%29 tanks per hour)

When both tanks were open for x hours, the amount of tank filled was (1/36)x.
When only tank A was open for y hours, the amount of tank DURING y was (1/12)y.
The whole tank filled was the SUM of these amounts of the filling job:
highlight%28%281%2F36%29x%2B%281%2F12%29y=1%29

The equations highlight-enclosed in red are your system to solve. You might want to simplify the job sum equation first, multiplying left and right by 36:
x%2B3y=36,
'
So now you can use the simpler system to solve for x and y:
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x%2B3y=36
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x%2By=14
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