SOLUTION: A plane flies at 170 mph for the first and last half hour of a flight. It flies at a higher constant speed for the rest of the flight. The route is 2020 miles. The plane is 920 mil

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Question 272981: A plane flies at 170 mph for the first and last half hour of a flight. It flies at a higher constant speed for the rest of the flight. The route is 2020 miles. The plane is 920 miles from the destination 2 hours before the end of the flight.
How many hours is the entire flight?
I have gotten that it is between 4-5 hours but I cannot seem to workout the exact amount. Any help would be great and much appreciated!!
Answer by dabanfield(803) About Me  (Show Source):
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A plane flies at 170 mph for the first and last half hour of a flight. It flies at a higher constant speed for the rest of the flight. The route is 2020 miles. The plane is 920 miles from the destination 2 hours before the end of the flight.
How many hours is the entire flight?
I have gotten that it is between 4-5 hours but I cannot seem to workout the exact amount. Any help would be great and much appreciated!!
The last 920 miles are covered in 2 hours. The last half hour is flown at 170 mph so the distance covered in the last half hour is 170*.5 = 85 miles. So in the 1.5 hours prior to the last half hour the plane covers 920-85 = 835 miles. The speed of the plane then is 835/1.5 = 556.66 mph. This means then that for the entire distance except that covered by the first and last half hours is
2020 - 85 - 85 =
2020 - 170 = 1850
The time taken for this part of the flight is 1850/556.66 = 3.32 hours.
So the entire flight takes .5 + 3.32 + .5 = 4.32 hours