Question 27198
I want to start my stopwatch at a time {{{t[0]}}} and I want to stop my
stopwatch at {{{t[1]}}} when the signal catches up with the satellite.
When should {{{t[0]}}} be?
I want it to be when the signal is sent from Earth because both the satellite
and the signal are active then.
Where is the satellite when the signal is sent? It has travelled 
{{{d[sat] = r[sat] * t[sat]}}}
r[sat] = 3 km/sec
t[sat] = 100 days x 24 hrs/day x 60 min/hr x 60sec/min = 8,640,000 sec
{{{d[sat] = 3 * 8640000}}}
{{{d[sat] = 25920000}}} in km
That's the headstart the satellite has.
Now start the stopwatch. It's t[0]
For the signal:
{{{d[sig] = r[sig] * t[sig]}}}
t[sig] is going to be the same as t[sat] because t[1] - t[0] is the same 
for both of them, so just call it t.
{{{d[sig] = 3 *10^5 * t}}}
d[sig] is equal to d[sat] + the headstart the satellite has
{{{d[sat] + 2.592 *10^7 = 3 * 10^5 * t}}}
for the satellite
{{{d[sat] = 3 * t}}} (t runs from t[0] to t[1])
substitute {{{d[sat] = 3 * t}}} in {{{d[sat] + 2.59 *10^7 = 3 * 10^5 * t}}}
{{{(3 * t) + 2.592 *10^7 = 3 * 10^5 * t}}}
subtract 3*t from both sides and rearrange
{{{299997 * t = 2.592 * 10^7}}}
t = 86.3 sec approximately
There are lots of chances for error, but I think my approach is OK