Q. A plane flies round- trip between Los Angeles and Namulevu,Vanuavinaka.The plane takes off at 12:50 P.M. Los Angeles time and lands at 6:50 P.M. Namulevu time.On the return trip, it takes off at 1:50 A.M. Namulevu time and lands at 6:50 P.M. Los Angeles time.Assume that the flight time is same in both the directions and that the plane flies in a straight line at an average speed of 520 mi/hr.

i> What is the time difference between Los Angeles and Namulevu and approximately where on globe is Namulevu located?

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Let the actual flight time, as measured by the passengers, be `T` .

Time difference between the two cities, `DeltaT` = Namulevu time - Los Angeles time. The `DeltaT` will be positive if Namulevu is east of Los Angeles.

The actual time of ﬂight from Los Angeles to Namulevu is then the difference between when the plane lands (LA times) and when the plane takes off (LA time):

`T = (18:50 - DeltaT ) - (12:50) = 6:00 − DeltaT ` ........(i) (in 24 hour format)

Again, changing to LA time,the return ﬂight time can be found from

`T = (18:50) - (1:50 - DeltaT ) = 17:00 + DeltaT` ............(ii)

Solving (i) and (ii):

`17:00 + DeltaT = 6:00 - DeltaT`

`rArr 2DeltaT = 6:00 - 17:00`

`rArr DeltaT = -5:30`

Since this is a negative number, Namulevu is located west of Los Angeles.

Hence, from (i),`T = 6:00 − DeltaT = 11 : 30` , or eleven and a half hours.

The distance travelled by the plane is given by `d = vt `

`= 520 (mi)/(hr)*(11.5 hr) = 5980 mi.`

To find the approximate location of Namulevu on the globe, we have to draw a circle around Los Angeles with a radius of 5980 mi, and then look for where it intersects with longitudes that would belong to a time zone `DeltaT` away from Los Angeles. Since the Earth rotates once every 24 hours and there are 360 longitude degrees, then each hour correspondsto 15 longitude degrees, and then Namulevu must be located approximately `15^o * 5.5 = 83^o` west of Los Angeles, or at about longitude 160 east. The location on the globe is then latitude `5^o ` , in the vicinity of Vanuatu.

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