Question 995046
This type of travel rates problem is too common, and it deserves a generalized, symbolic solution.  The solution done here will be done for AMOUNT of time.


The data table will imply the needed variables.
<pre>
Two vehicles leaving at different times going in the same direction.

VEHICLE           speed           time        distance
Early slow        r               t+h          d
Late fast         R               t            d

VARIABLES
Known: r, R, h
Unknown: t, d
Fast late vehicle departs h amount of time after early slow vehicle departs, and so the fast but later vehicle travels for less time.
Variable distance d is the catchup distance.

{{{R>r}}}

GOAL:  Solve for t
</pre>
{{{system(r(t+h)=d,Rt=d)}}}

{{{r(t+h)=Rt}}}
{{{rt+rh=Rt}}}
{{{Rt-rt=rh}}}
{{{t(R-r)=rh}}}
{{{highlight(highlight(t=rh/(R-r)))}}}