Question 857431
Uniform Rates, work of peeling potatos.
R*T=P for rate in potatos per minute, time in minutes, potato count peeled.
Let t = amount of time for Janet to catchup  with Butch, or the time that both have peeled the same number of potatos.
Let p = amount of potatos each person has peeled, WHEN EACH HAS DONE THE SAME NUMBER OF THEM.


_____________rate_________time_________Potatos Count
Butch________3____________t+4__________p
Janet________5____________t____________p


The rate equation gives us these two equations:
Butch: p=3(t+4)
Janet:  p=5t


You used x, while I used t.  same meaning.  Your point of view of time is a little different but no matter.  Janet's time is 4 minutes less than Butch; Butches time is 4 minutes more than Janet's.


The two expression for p are equal.
{{{highlight_green(3(t+4)=5t)}}}
{{{3t+12=5t}}}
{{{12=5t-3t}}}
{{{2t=12}}}
{{{highlight(t=6)}}} minutes for Janet to catch up with Butch, meaning when they both peeled the same number of potatos.