Question 986178
This exact TYPE of question is frequent.


<pre>

Train     speed     time     distance
EARLY      r        t+h      d
LATER      R         t       d

KNOWN VARIABLES:
r,R,h.
{{{r<R}}}.
h is the delay which occurs in hours before the later train starts from the departure location.
UNKNOWN VARIABLES:
t,d.
t is the time during which the later train travels and overtakes the early train.

</pre>


Goal is to solve for t and d.

{{{system(r(t+h)=d,Rt=d)}}}


The equality of formulas for d gives
{{{rt+rh=Rt}}}
{{{rh=Rt-rt}}}
{{{rh=(R-r)t}}}
{{{highlight(t=rh/(R-r))}}}
-
Use formula for t to find d.
{{{d=R(rh/(R-r))}}}
{{{highlight(d=Rrh/(R-h))}}}


The problem is now fully solved in symbolic form.  Substitute the given values and evaluate t and d.