Question 1055890
I am starting this but may leave it unfinished.  I am showing here a data table.   Note that from slowest to fastest, P, Q, R.  Naturally, R can depart last because he is the fastest and is expected to overcome distance traveled of P and Q.  Assumes that a and b are positive real numbers.  Let x be the travel time for R to catchup distance d to P and Q.


<pre>
TRAVELER      RATE        TIME       DISTANCE
P             a           t+p+x         d
Q             a+b         p+x           d
R             a+2b        x             d
</pre>

Travel Rate Rule using speed S is  S*T=D.
The UNKNOWN variables in the example must be just t, x, and d.  Question's interpretation mean you want to find the solution for x.


Several careful algebra steps, and after doing those  on paper, {{{highlight(x=(ap+bp+ab)/(2b))}}}