A train problem. How does a train problem involve pi you ask? Read on!
My train engine has a wheel base of 48.5 feet and the train engine's drive wheel has a diameter of 33 inches. There are no train cars behind the train engine. The wood fired fire box is operating at 400 degrees Fahrenheit. The track width is 4 foot 8.5 inches.
Attached to the back of my train engine is a hose. This hose is special. As the hose is pulled from its reel, it becomes perfectly straight and does not deform to weight, pressure, or temperature. The hose has an inside diameter of 200 millimeters.
My train engine leaves my train station at 12:24 pm on 3.14 (pi day) and instantly has a constant velocity of 68 mph. The track was laid in a perfectly straight line for 25 miles on a heading of 287 degrees true. At the 25 mile mark the track makes an immediate 38 degree turn to the left and continues for another 10 miles. Amazingly this train engine is built to withstand this kind of force.
The train engine drive wheel turns exactly 6,111 revolutions and the train instantly stops. The hose is cut at the starting line and one end of the hose is sealed, resulting in no volume gain or loss. Water is then poured into the open end of the hose, entirely filling the hose, with no loss due to bubbles, aliens, me being thirsty, or any other source. How many gallons of water are in the hose?
You should have an eight digit number: ABCDEF.GH
Final latitude: 3,980,365.55 + ABCDEF.GH
Final longitude: 9,741,637.45 - ABCDEF.GH
Truncate all intermediate calculations to 7 digits. I give you pi to 7 digits.
Truncate the number of gallons to 2 digits.
If it matters to you, I did all the math in MS Excel.
You can check your answers for this puzzle on GeoChecker.com.