Math Is Fun Forum

Avva

Member

Registered: 2009-02-25

Posts: 41

Related Time Rates Problem

Liquid is leaking from a small hole in a vessel full with the liquid. The volume of the liquid changes at the rate of (0.4t-40)cm³/sec.

find:
1- The volume of the vessel
2- When the vessel becomes empty?
given that the volume of the liquid was 980cm³ after 30 seconds from the start of leaking.

PLEASE Explain your answer and if you can give me guide steps to solve problems like this '

MANY THANKS in Advance:D.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Related Time Rates Problem

Hi Avva;

Have you had differential equations before? What are you studying right now?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Avva

Member

Registered: 2009-02-25

Posts: 41

Re: Related Time Rates Problem

Yup, I have. we're studying principles of  differential and integral calculus I solve related time rates problems but this kind is odd according to me and I can't figure it out I used to solve Time and Distance problems using differential equations . please help me solve this kind.Tx 4 ur reply

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Related Time Rates Problem

Here is why I do not think it is a related rate problem. You have one rate of change but you are not being asked to find another. I think it is a differential equation. Anyway I solve it like this:

Solve by separating the variables.

To determine c you plug in and solve:

So the solution of the DE is:

To answer the first question you plug in t=0.

The Volume = 2000 cm^3

To answer the second question you set V(t) =0

Solve for t and you get t = 100 and t = 100.

The vessel will be empty in 100 seconds.

Now please understand I have solved the DE correctly and if this is a DE problem then you are home free.
But if it is a related rate problem then I went down the wrong road! I can say that this is how I would answer the question.
So if it is wrong we both would get it wrong!

What textbook did this come out of? Title and author please.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Avva

Member

Registered: 2009-02-25

Posts: 41

Re: Related Time Rates Problem

thanks for ur reply I appreciate it . I think that this is the right solution , I have been searching for a related time problem like this one but I found none but at the same time I didn't think that the sol might be that easy one.The textbook is my school book and we're in secondary school so the ministry in our country  prepare it without writing the references. Many Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Related Time Rates Problem

Hi Avva;

Glad to help. I only hope I guessed at the type of problem correctly.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.