Associated Topics || Dr. Math Home || Search Dr. Math

### Variation on Combined Work

```Date: 06/13/2002 at 01:45:33
From: Vibhuti Dhand
Subject: word problems in linear equations in two variables

It takes 12 hours to fill a swimming pool using two pipes. If the
larger pipe is used for 4 hours and the smaller for 9 hours, only half
of the pool is filled.

How long would it take for each pipe alone to fill the pool?
```

```
Date: 06/13/2002 at 13:18:07
From: Doctor Ian
Subject: Re: word problems in linear equations in two variables

Hi Vibhuti,

It sounds to me like you're saying:

A large pipe can fill 1/2 a pool in 4 hours.

A small pipe can fill 1/2 the same pool in 9 hours.

Together, the pipes can fill the pool in 12 hours.

But this can't be right, because then the answers are trivial:
The large pipe can fill the pool in 8 hours, and the small one
can fill it in 18.

Or are you saying:

If you run a large pipe for 4 hours, and run a small pipe
for 9 hours, you can fill 1/2 a pool.

If you run both pipes together for 12 hours, you can
fill the whole pool.

Is that correct?

If so, let's say that the pool holds G gallons, that the large pipe
contributes R gallons per hour, and the small pipe contributes r
gallons per hour.  Then

4R + 9r = G/2           (First condition)

12(R + r) = G            (Second condition)

Doubling the first equation gives us

8R + 18r = G

12(R + r) = G

Two things that are equal to the same thing are equal to each
other, so

8R + 18r = 12(R + r)

So you can use this to find out the ratio of the rates for the
two pipes,

R = kr

Then you can substitute that back into the equation

12(kr + r) = G

to find out how long the smaller pipe needs to fill the whole
pool; which will tell you how long it takes the larger pipe to
fill the whole pool.

Can you take it from here?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Linear Equations
Middle School Equations
Middle School Ratio and Proportion

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search