Airspeed calculation

[Guest]

I am more interested in the equation ( which I can use from now on ) rather than just the answer !!
A Cessna 210 cruises @ 165 knots, which is 189.75 mph, and accordingly requires 3 hrs and 15 minutes to go from Southeast Texas to Nashville, Tennessee ( 195 minutes )
A Piper Comanche 250 takes 3 hrs and 21 minutes, which is just 6 minutes longer ( 201 minutes ).
What is the equation thru which I can compare these two & find out the cruise speed of the Comanche, without using the trial & error method ?
I HAVE tried the comparison, 165 kts is to 195 minutes = XXX kts is to 201 minutes, but that yields 170 kts, a FASTER airspeed, which would of course require LESS time than the 195 minutes required for the 165 knot airspeed.
I've tried a few variants, but I haven't gotten there yet.

[Guest]

The formula you want to use is
speed = distance/time
Which rearranges to
distance = time x speed
(so if I'm travelling for time=2 hours at speed = 100 miles per hour, my distance = 2*100 = 200 miles)

The distance travelled by aircrafts A and B are the same so the product of their time and speed must be the same
(time taken by A) x (speed of A) = (time taken by B) x (speed of B)
So rearranging gives us the formula
(speed of A) = (time taken by B) x (speed of B) / (time taken by A)

For the specific problem you give we have
speed of Piper Comanche = (195/60 hours) x (189.75 miles per hour) / (201/60 hours)
which is 184.0... miles per hour or 160.0... knots

Hope this helps,

R. Baber.