<PRE><B>Question 1207799</B>
&lt;br&gt;
Together two pumps can do the job in 5 hours.
I understand this:
Pump 1 + pump 2 = 5 hours.
Is this right?&lt;br&gt;
We don&#39;t know what it means, so perhaps we don&#39;t know if it is right.&lt;br&gt;
But in fact we know it can&#39;t be right, because the equation literally says the sum of two things is some number of hours.  If you are adding two things and the sum is some number of hours, then the two things you are adding must be hours.  Pumps are not hours.&lt;br&gt;
Smaller pump = x
Larger pump = x - 4
Is this right?&lt;br&gt;
Again we don&#39;t know, because we don&#39;t know what it means.  Are &quot;x&quot; and &quot;x-4&quot; the names of the two pumps?  I doubt it.&lt;br&gt;
No matter how much experience you have working math problems, you are always potentially in trouble if you don&#39;t start with clear and precise definitions of the variables and expressions you are going to use.&lt;br&gt;
The standard method for solving &quot;working together&quot; problems is to write an equation that says the sum of the fractions of the job that each worker does in some amount of time is equal to the fraction of the job that they do together in that time.&lt;br&gt;
The problem says that the larger pump can do the job in 4 hours less than the smaller pump.  So the proper definitions of &quot;x&quot; and &quot;x-4&quot; are&lt;br&gt;
Let x = # of hours the smaller pump takes to do the job alone
Then x-4 = # of hours the larger pump takes to do the job alone&lt;br&gt;
(Compare that to the &quot;definitions&quot; you show for x and x-4....)&lt;br&gt;
Next, from there (as you tried to do in your setup),&lt;br&gt;
Then 1/x = fraction of job done by smaller pump in 1 hour
And 1/(x-4) = fraction of job done by larger pump in 1 hour&lt;br&gt;
Our equation is going to say &quot;fraction done by one pump in 1 hour, plus fraction done by other pump in 1 hour, equals fraction done together in 1 hour&quot;.  Since they can do the job together in 5 hours, the fraction of the job they do together in 1 hour is 1/5.&lt;br&gt;
So, finally,&lt;br&gt;
{{{1/x+1/(x-4)=1/5}}}&lt;br&gt;
That completes the setup.  Actually solving that leads to a very ugly quadratic equation, so I would use a tool like a graphing calculator to find the answer.&lt;br&gt;
But perhaps what you were looking for was help in doing the setup....&lt;br&gt;
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