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By Golly, I DID Use It in Real Life!. Corrie Bergeron Math Awareness Week 2006. Two real-life examples. Picking a local moving company Planning a cross-country flight. Picking a Moving Company. Company A $45 / hr Charge only for time spent on-site Company B $35 / hr
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By Golly,I DID Use Itin Real Life! Corrie Bergeron Math Awareness Week 2006
Two real-life examples Picking a local moving company Planning a cross-country flight
Picking a Moving Company • Company A • $45 / hr • Charge only for time spent on-site • Company B • $35 / hr • Charge from the time they leave their shop until they return (about 1.5 hours extra)
Which to choose? • At $45/hr, A is cheaper for short jobs since they only charge for time on site • B is cheaper for a long job - $10/hr savings eventually offset 1.5 hr “transit” charge • Which will be cheaper for MY move? • Depends on how long it’s going to take to move me!
I saw the light – use ALGEBRA! • Cost is a function of time • Find the time where both companies cost the same. If my move will take less time than that, then Company A will be cheaper. • Let H = Number of hours the job will take • Company A cost = 45xH • Company B cost = 35x(H + 1.5) • So 45xH = 35x(H + 1.5)
Solve for H 45xH = 35x(H + 1.5) 45xH = 35xH + 35x1.5 45xH = 35xH + 52.5 Move the 35H to the other side:45xH – 35xH = 52.5 10xH = 52.5 H = 5.25 So if the job takes longer than 5.25 hours, Company B is cheaper!
Point A to Point B Point B: Litchfield airport Point A: Flying Cloud airport
2. Correct for Wind If you just fly the true course, the wind will blow you off-target
You have to “crab” into the wind Wind correction angle depends on your airspeed and course, and the wind speed and direction.
Plan the flight… • E6B gives wind correction angle and ground speed from true course, airspeed, and wind speed and direction • Compass Course (direction to point the nose) = True Course (from chart) +/- Wind Correction Angle (from E6B) +/- Magnetic Deviation (from chart) • Time Enroute = Distance (measured from chart) / Ground Speed (from E6B)