Math Is Fun Forum

shivusuja

Member

Registered: 2006-09-14

Posts: 56

Quadratic Equation

Please Help Me Out This Problem:
Two Pipes Running Together Can Fill A Tank In 40/3 Minutes. If One Pipe Takes 3 Minutes More Than Other To Fill A Tank . Find The Time Taken By Each Pipe To Fill The Tank.

Thanks In Advance

gnitsuk

Member

Registered: 2006-02-09

Posts: 121

Re: Quadratic Equation

The time taken for each pipe to fill the tank will depend on the volume of the tank, call this V and it is a constant for our problem. So our final answer will have V in it.

Let the pipes be called A and B.

Let

time for pipe A to fill the tank

Let

time for pipe B to fill the tank

Let

volumetric flow rate of pipe A in cubic measures per minute

Let

volumetric flow rate of pipe B in cubic measures per minute

So we have the following four equations:

(1)   

(2)   

(3)   

(4)   

Substituting (1) and (2) into (3) we have

(5)   

Rearranging (4) we have

=>

Substituting this value into (5) gives us

=>

=>

=>

=>

Using the quadratic formula gives us

6481 is prime so the root won't simplify. This gives you a value for Ar which you can in turn substitute into (1) to find At and then Bt by (3).

Last edited by gnitsuk (2007-01-28 23:16:43)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Quadratic Equation

Hi;

I am getting a different answer. Let t be the time it takes the first pipe.

Solving:

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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.