Math Puzzle for September 13, 2024

Flying first class, working business class, living coach

Tristan and Layla depart Dothan, Alabama to visit their Nonno in Alameda, California.
The distance from Dothan to Alameda is 2,500 nautical miles.
The headwind W , flying from Dothan to Alameda, is a constant 80 knots (nautical miles per hour).
The pilots have the option of selecting an airspeed V (300 knots < V < 600 knots ) by adjusting their power.
If the pilots increase their speed V , the engines require more power and burn more gallons of fuel per hour.
The relationship between airspeed V and the fuel consumption rate, i.e. , gallons per hour ( gph ) is a quadratic.
The pilots are given the chart below to determine the quadratic relationship between airspeed V and gph .

The pilots, environmentalists by nature and cognizant of global warming, want to total minimize fuel burn.
The pilots have the option of selecting an airspeed V conducive to saving fuel and reducing emissions.
The total quantity Q of fuel consumed is equal to the rate ( gph ) multiplied by the total flying time ( t ).
Total flying time ( t ) is equal to the distance, i.e., 2500 nm, divided by the ground speed GS , i.e., ( V − W ).
Consuming minimum fuel, their environmentally friendly numbers are …

Airspeed V = _________ knots Consumption Rate = _________ gph

Time En Route = _________ hours Total Fuel Consumed = _________ gallons

First correct answers sent to JeffreyRSmith@aol.com win a valuable gift card for Tucker’s Ice Cream of Alameda.

Last week’s winner was John Lovato with Amplitude a = 1.14421866 units.

Jeff Smith is a former Math teacher and a retired US Navy Lieutenant Commander. Reach him at JeffreyRSmith@aol.com .

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