Question 1126374
<pre>
           Rate in piece per hour

Bill      {{{1/(t-1/4)}}}

Will      {{{1/t}}}

Together  {{{1/4}}}
</pre>

Together rate is the sum of their individual rates.

{{{1/(t-1/4)+1/t=1/4}}}


{{{4t(t-1/4)(1/(t-1/4)+1/t)=4t(t-1/4)(1/4)}}}


{{{4t+4(t-1/4)=t(t-1/4)}}}


{{{8t-1=t^2-t/4}}}


{{{32t-4=4t^2-t}}}


{{{highlight_green(4t^2-33t+4=0)}}}


Using general solution for quadratic equation,
{{{t=(33+- sqrt(1025))/8}}}


The PLUS-form is necessary.


{{{highlight(t=(33+sqrt(1025))/8)}}}------the time for Will alone.
Use this to find the time for Bill alone.