Question 668700
If one pump can fill a pool in 16 hours and if two 
pumps can fill the pool in 6 hours, how fast can the 
second pump fill the pool?
<pre>
The filling rate of the first pump is 1 pool per 16 hours, or

{{{(1_pool)/(16_hours)}}} or {{{1/16}}}pool/hour.

The filling rate of the second pump is 1 pool per x hours, or

{{{(1_pool)/(x_hours)}}} or {{{1/x}}}pool/hour.

Their combined filling rate of both pumps is 1 pool per 6 hours, or

{{{(1_pool)/(6_hours)}}} or {{{1/6}}}pool/hour.

The equation comes from:

            {{{(matrix(5,1,

Filling, rate, of, first, pump))}}} + {{{(matrix(5,1,

Filling, rate, of, second, pump))}}} = {{{(matrix(6,1,

Combined, filling, rate, of, both, pump))}}}
 
                    {{{1/16}}} + {{{1/x}}} = {{{1/6}}}

Solve that by multiplying through by the LCD of 48x 

                    x = {{{48/5}}}
                               
                    x = 9.6 hours

or 9 hours and 36 minutes.

Edwin</pre>