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

[puma072806]

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.

 

[phinds]

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?

 

[skeptic2]

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?

 

[puma072806]

Skeptic2 is right as far as interpreting the problem goes. Can anyone help me out?!
Thanks.

 

[haruspex]

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?

 

[Michael Redei]

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)?

 

[SammyS]

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.

 

[puma072806]

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.

 

[skeptic2]

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?

 

[puma072806]

6 liters per second
So would it take six hours to fill the tank if only B were open? Or 5?

 

[phinds]

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.

 

[skeptic2]

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?

 

[puma072806]

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!