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### Filling a Tank

```Date: 12/19/2002 at 05:58:03
From: Shabnam
Subject: Filling a tank

A tank is filled by two pipes. The smaller pipe alone will take 24
minutes longer than the larger pipe and 32 minutes longer than when
booth pipes are used. How long will each pipe take to fill the tank
alone?
```

```
Date: 12/19/2002 at 09:44:12
From: Doctor Ian
Subject: Re: Filling a tank

Hi Shabnam,

This is a new twist on an old problem; see the Dr. Math FAQ:

Working Together
http://mathforum.org/dr.math/faq/faq.working.together.html

The standard formula is that if the first entity takes A units of
time,and the second takes B units of time, then together they take

A * B
-----
A + B

units of time. If the small pipe takes x minutes to fill the tank,
then the larger one takes (x-24) minutes, and the combined time is

x * (x-24)
----------
x + (x-24)

But this has to be (x-32) minutes, so

x * (x-24)
---------- = (x-32)
x + (x-24)

x(x - 24) = (2x - 24)(x - 32)

x^2 - 24x = 2x^2 - 64x - 24x + (24)(32)

0 = x^2 - 64x + (24)(32)

Can you take it from here?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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