I've missed the deadline, I'm afraid. But only because my hard copy of The Actuary turned up in my office today - postal services to the colonies remain a bit slow at times. Perhaps the delivery plane was up against headwinds, not entirely unlike the subject of puzzle 615 (The Actuary, March) being up against the tide:
"A ship is battling against a strong tide to get to safety. It uses 6 gallons of fuel every hour and sails at 17 mph in still conditions. The ship is 24 miles from safety and the flow against it is 8 mph. The ship has 16 gallons of fuel remaining.
How much will there be when it reaches the shore?"
When I read the puzzle, I thought the answer is probably zero. That is, the net forward speed is 9 knots* and the ship needs to cover 24 miles. That is 2 hours 40 minutes and burning 6 gallons of fuel per hour means 16 remaining gallons would be used up exactly in 2 hours 40 minutes.
But then I thought that the answer cannot be determined from the information provided. Tidal flows are not constant - the height of the tide rises and falls in a pattern very similar to a sine wave.
In most locations on the earth, there are two tides a day. When the tide is turning, the tidal flow is nil, then it picks up speed to be at its maximum roughly halfway between the tidal peak or trough, then slows again to be nil at the next turn. Local geographical features can alter this. The puzzle does not tell us anything about how a tidal rate of currently 8 knots* will change over the next 2 hours 40 minutes. The salt in my blood tells me it won't remain constant!
So I conclude that the fuel remaining when the ship reaches shore will be a positive non-zero quantity - the captain would slow the ship to preserve fuel until the tidal flow slowed to approach zero (or reverse) and then bring the ship in with fuel to spare. Simple.
*Knots - I know the question setter said mph but when it comes to nautical measures, 1 minute of latitude is 1 nautical mile (usually simply referred to as 1 mile). A speed of 1 mile per hour is 1 knot. A land statute mile is not the same as a nautical mile.
David McNeice 24 March
