Interesting problem I have met before. I think this is worth looking at. I shall try and get a more elegant solution.
Imagine 2 different aeroplanes flying in formation. One slows down so they diverge. The divergence must be 8 minutes, or 8/60 hours by the time the slower one gets to destination.
Speed=Distance/Time. Or Time= Distance/Speed
Let 'x' be faster aeroplane and 'y' slower aeroplane.
So as Time=Distance/Speed, but slower aeroplane time, Ty, is Tx+8(minutes, or 8/60 hours).
Therefore D/200= D/260 + 8/60
Multiply top line by 200 x 260 x60 to get rid of the nasty fractions,
(D x 260 x 60) = (D x 200 x 60) + (8 x 200 x 260)
3600 x D = 416000
D= 115.5
Testing, 260kts, 115.5 miles takes 26 2/3 minutes
At 200 kts, 115.5 miles takes 34 2/3 minutes
Bingo. Harder one please!
Last edited by Rainboe; 3rd August 2009 at 20:39.