Algebra problem with several variables
Category: Science > Math
Asked by: downtheline-ga
List Price: $20.00
14 Dec 2003 19:23 PST
Expires: 13 Jan 2004 19:23 PST
Question ID: 287206
I have a math problem. I've often taken the United to Kona, Hawaii flight and they play a game called halfway to hawaii. The pilots give you the following data: total miles to Kona from SF, average speed of each half of the flight, headwind/tailwind for each half (which you simply add/subtract from speed), exact takeoff and estimated landing time. What is the algebraic formula to solve this problem?? The last time I took the trip, the following facts resulted in a the halfway point at 10:03 AM Hawaii time (I couldn't solve for it even with the facts!): 7:30 AM takeoff (HI time), 5 hrs 15 minutes total flight time, 485 MPH for first half/462 for second, 33 and 45 MPH head wind (so subtract) for 1st/2nd half. Thanks for helping as it's been driving me crazy that I can't figure it out.
Re: Algebra problem with several variables
Answered By: endo-ga on 14 Dec 2003 20:05 PST
Hi, Thank you for your interesting question! I'd love to fly to Hawaii and have fun answering maths questions at the same time :) Anyways here is the calculation, which should allow you to answer what you're looking for. First you need to calculate the total distance covered. Lets call this distance 'd'. We know that the time needed to travel half of d at 452 miles per hour (485-33) added to the time needed to travel half of d at 417 miles per hour (462-45) totals 5.25 hours Since time = distance / speed we have: d x ( 1/(2 x 452) + 1/(2 x 417)) = 5.25 hours d x ( 1/904 + 1/834) = 5.25 hours d x (834+904)/(834x904) = 5.25 hours d = 5.25 x 834 x 904 / (834+904) = 2277.42 miles Half way is thus: 2277.42/2 = 1138.71 miles Time needed to fly 1138.71 miles at 452 miles per hour: 1138.71 / 252 = 2.519 hours = 2 hours 31 minutes 9 seconds Thus if we add this to the takeoff time of 7:30 we get 10:01. Give or take 30 seconds from each (since the times are not given to the second) and take into account that the speeds are approximate, then you have your answer. I hope this answers your question. If something is unclear of if you need any clarifications, please do not hesitate to ask. Thanks. endo
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