George took a nonstop flight from Dallas to Los Angeles, a total flight distance of 1,233 miles. The plane flew at a speed of 460 miles per hour for the first 75 minutes of the flight and at a speed of 439 miles per hour for the remainder of the flight. To the nearest minute, for how many minutes did the plane fly at a speed of 439 miles per hour?

The correct answer is: 90

The total distance between Los Angeles and Dallas is 1233 miles.
So, total distance covered = 1233 miles.
Initially,
Speed of the plane = 460 miles per hour
Time taken = 75 minutes
We convert the time in hours as the speed is given in miles per hour.
As, 60 minutes = 1 hour
So, we get, 75 minutes =   =   = 1.25 hours
Thus, time taken = 1.5 hours
We know,

Rewriting the equation , we have

Thus, the distance travelled initially is given by

Thus, the distance covered by the flight in the first 75 minutes while  the speed was 460 miles per hour = 575 miles
Next,
Remaining distance to travel = 1233 – 575 = 658 miles
For the second part of the journey,
Speed of the plane = 439 miles per hour
Distance travelled = 658 miles
Rewriting the above formula, we get

Using the above quantities, we get

Converting the time into minutes, we have,

Thus, the number of minutes for which the plane flies at speed 439 miles per hour = 90 minutes




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Note:
The relation between speed, distance and time given by the relation above is very important. There could be many such questions formed which ask us to calculate any of the three quantities with certain conditions involved.