Note: The posted co-ordinates are bogus.
Chookies and Muzza were both out caching one day in the same area. Muzza was on North-South Road while Chookies were on East-West road. Muzza was on his bicycle exactly 9.305 km.s South of the intersection of the two roads. Chookies were in their car and exactly 7.354 km.s West of the intersection of the two roads. Muzza headed north at a constant 16.7 km.s per hour exactly, while Chookies headed East at a constant 100.7 km.s per hour exactly. (See the diagram).
North-South road runs precisely in a northerly/southerly direction (not magnetic north) while East-West road runs precisely in an easterly/westerly direction. They intersect at 90° and both roads are absolutely straight. There was no traffic to slow them down.
At the time that they were the closest to each other, Muzza was A.AAA km.s from the intersection, while Chookies were B.BBB km.s from the intersection.
The cache is placed at S 37° 4A.AAA E 145° 0B.BBB - It is a 100 ml plastic test tube. BYO Pen.
Note: This is not a puzzle as such, just a fairly simple mathematical problem to be solved. You will need to be accurate to 3 decimal places in your final answer, so the intermediate results will need to be done to more places. You can solve it purely with maths, or you might utilize the capabilities of a spreadsheet program if you're not into simple differentials.
If you are uncertain of your answer and want confirmation, please feel free to email me your calculated co-ordinates and I will verify them for you.