MHB Emptying and filling a tank word problem.

[paulmdrdo1]

I just want to make a sanity check here.

here's the problem

One pipe can fill a tank 45min and another can fill it in 30 min. If these two pipes are open and a third pipe is draining water from the tank, it takes 27 min to fill the tank. how low will it take the third pipe alone to empty a full tank?

this is how I solved it. But I'm dubious about the real life scenario I'm picturing in my head right now.

$\frac{1}{45}\times 27+\frac{1}{3}\times 27-\frac{1}{t}\times 27=1$ where t is the time required for the third pipe to empty the tank by itself.

answer $t=54$min

if the Filling and the emptying of the tank is simultaneously happening how can we say that the tank will reach the full state? I'm confused! please help me picture this correctly.

 

[soroban]

Hello, paulmdrdo!

I just want to make a sanity check here.

One pipe can fill a tank 45min and another can fill it in 30 min.
If these two pipes are open and a third pipe is draining water
from the tank, it takes 27 min to fill the tank.
How long will it take the third pipe alone to empty a full tank?

This is how I solved it. But I'm dubious about the real life
scenario I'm picturing in my head right now.

$\frac{1}{45}\cdot 27+\frac{1}{3}\cdot 27-\frac{1}{t}\cdot 27\;=\;1$ . Correct!
where t is the time required for the third pipe
to empty the tank by itself.

Answer: t = 54 min. . Right!

If the filling and the emptying of the tank is simultaneously
happening, how can we say that the tank will reach the full state?
I'm confused! please help me picture this correctly.

Think about it . . .

Pipes A and B are filling at a faster rate than pipe C is draining.
Of course, the tank will eventually be filled.

 

[MarkFL]

Another way to look at it is that in 270 minutes, the first pipe can fill 6 tanks, the second pipe can fill 9 tanks and with the drain open 10 tanks will be filled. This means the drain can empty 9+6-10=5 tanks in 270 minutes or 1 tank every 54 minutes.