Emptying and filling a tank word problem.

In summary, the conversation discusses the time required for a third pipe to empty a full tank while two other pipes are simultaneously filling it. Through a series of equations, it is determined that the third pipe would take 54 minutes to empty the tank by itself. There is also a brief discussion about the scenario in real life.
  • #1
paulmdrdo1
385
0
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.
 
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  • #2
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 [tex]t[/tex] 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.
 
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  • #3
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.
 

FAQ: Emptying and filling a tank word problem.

What is the purpose of the "Emptying and filling a tank word problem" in science?

The purpose of this word problem is to demonstrate the concept of rate of change and how it can be applied to real-world situations. It also helps students practice problem-solving and critical thinking skills.

What are the key components of an "Emptying and filling a tank word problem"?

The key components include the initial volume of the tank, the rate at which the tank is being filled or emptied, and the time it takes for the tank to be filled or emptied.

What is the formula for solving an "Emptying and filling a tank word problem"?

The formula for solving this type of word problem is: final volume = initial volume ± (rate of change x time). The plus or minus sign depends on whether the tank is being filled or emptied.

What are some common mistakes students make when solving an "Emptying and filling a tank word problem"?

Some common mistakes include using the wrong units for time or rate, forgetting to account for changes in volume over time, and not properly setting up the equation to solve for the final volume.

How can "Emptying and filling a tank word problems" be applied to real-life situations?

These types of word problems can be applied to situations such as filling a swimming pool, draining a bathtub, or filling a gas tank. They can also be used in engineering and environmental science to calculate rates of change in water levels or chemical concentrations.

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