What is the Time to Fill a Tank with Pipe B Only?

In summary, the problem is that the volume of water flowing through pipe A is 5 times greater than the volume flowing through pipe B. This causes the tank to fill in 4 hours if both pipes are flowing, but it would take 5 hours if only pipe B were flowing.
  • #1
puma072806
7
0
I understand this is a basic problem. For some reason I just can't wrap my head around it. Any help is appreciated.

Homework Statement


Water flows through Pipe A five times faster than through Pipe B. When water flows through the both pipes a tank would be filled in 4 hours. How long will it take to fill a tank if only Pipe B opened?



Homework Equations





The Attempt at a Solution


Pipe A: (5x)
Pipe B: (x)
Time: four hours.
 
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  • #2
So if both pipes flow, it takes 4 hours but if only pipe B flows then it ALSO takes 4 hours ? Does that seem likely to you?
 
  • #3
I presume the problem means to say that the volume of water passing through pipe A is 5 times greater than the volume passing through pipe B. If water flows through both pipes, how many times the volume of pipe B is flowing?
 
  • #4
Skeptic2 is right as far as interpreting the problem goes. Can anyone help me out?!
Thanks.
 
  • #5
You've written that water flows through A at rate 5x and through B at rate x. If both flowing, what's the total rate? If that takes 4 hours to fill, how big is the tank?
 
  • #6
Your "attempt at a solution" says that pipe B delivers an amount x of water in a specified time to the tank. And pipe A delivers an amount 5x to the tank in the same time.

So how much do A and B deliver to the tank together (again, in the time we're using in these measurements)?
 
  • #7
puma072806 said:
Skeptic2 is right as far as interpreting the problem goes. Can anyone help me out?!
Thanks.
Answering Skeptic2's question at the end of his post should help you out.
 
  • #8
That's all the info that the problem gives.
Like I said I'm sure this is really easy for most people but I just can't wrap my head around it.
 
  • #9
So if A can deliver 5 liters per second and B can deliver 1 liter per second, how many liters per second can A plus B deliver?
 
  • #10
6 liters per second
So would it take six hours to fill the tank if only B were open? Or 5?
 
  • #11
puma072806 said:
6 liters per second
So would it take six hours to fill the tank if only B were open? Or 5?

You are not even close.

I've found that the best way to solve these "vague" problems is to make them specific and to do so in a way that simplifies the calculations.

Since you have a speed X and a speed 5X, ASSUME that your tank contains 6 liters (that the one plus the 5). From this you can deduce a value for X. Then you can go back and see what effect 1X would have, given that you know what effect 6X has.
 
  • #12
So if at 6 liters per second it takes 4 hours to fill the tank, how big is the tank?

Ans.: 4 hr x 3600 sec/hr x 6 liters / sec. = 86400 liters.

How many hours would it take to fill the tank at 1 liter/sec?
 
Last edited:
  • #13
Thanks everybody for all your help. I was able to figure it out with your help.

I got 24 hours as the final answer and the professor said it was correct.
Thanks again!
 

1. What is an algebraic word problem?

An algebraic word problem is a mathematical problem that is written using words instead of numbers or symbols. It requires the use of algebraic equations to solve for one or more unknown variables.

2. How do I solve an algebraic word problem?

To solve an algebraic word problem, you should start by identifying the unknown variable(s) and assigning a variable to represent it. Then, use the given information to write an algebraic equation or system of equations. Finally, use algebraic techniques such as substitution, elimination, or graphing to solve for the unknown variable(s).

3. Why are algebraic word problems important?

Algebraic word problems are important because they help develop critical thinking and problem-solving skills that are essential in everyday life and in many career fields. They also provide a practical application for algebraic concepts and help students understand the relevance of math in real-world situations.

4. What are some common keywords used in algebraic word problems?

Some common keywords used in algebraic word problems include "sum," "difference," "product," "quotient," "per," "more than/less than," "increased/decreased by," "total," "each," "together," "in all," and "perimeter/area/volume."

5. Can you provide an example of an algebraic word problem?

Sure, here's an example: A pizza shop charges a flat delivery fee of $5 plus $2 for each pizza. If the total cost for an order of 3 pizzas is $19, what is the cost of one pizza? First, we can assign the variable "x" to represent the cost of one pizza. Then, we can write the equation 5 + 2x = 19. Solving for x, we get x = $7. Therefore, the cost of one pizza is $7.

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