Question 1059932
Typical traveling catchup problem



{{{system(r=90,R=120,h=2)}}}

<pre>
                 RATE        TIME       DISTANCE
SLOW EARLY       r           t+h           d
FAST LATE        R           t             d
</pre>

The fast train catches up to the slow train when both have traveled distance d.  Question asks for {{{t}}}.


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


Solve the system for t.

{{{r(t+h)=Rt}}}
{{{rt+rh=Rt}}}

{{{rh=Rt-rt}}}

{{{rh=t(R-r)}}}

{{{t=(rh)/(R-r)}}}-----------the answer.