The distance between aerodromes A and B is 1000 Nautical Miles. At 09:00 an aircraft leaves for B with a speed of 300 Nautical miles per hour. At 09:30 another aircraft leaves for B from A with a speed of 400 Nautical miles per hour. At what approximate time will the second aircraft overtake the first aircraft?
A. 10:55
B. 11:15
C. 10:42
D. None of the above
The speed difference is 100
The first plane has a 1/2 hour head start, during which it went 150 miles.
so, it will take 1.5 hours to catch up.
...
To find the approximate time when the second aircraft overtakes the first aircraft, we can calculate their respective distances traveled at any given time.
Let's assume that the second aircraft overtakes the first aircraft after time 't' hours.
The first aircraft leaves at 09:00 and therefore, travels for 't' hours before being overtaken.
Distance traveled by the first aircraft = Speed * Time = 300 * t = 300t (nautical miles)
The second aircraft leaves at 09:30, which means it travels for (t - 0.5) hours before overtaking the first aircraft. This accounts for the half-hour time difference.
Distance traveled by the second aircraft = Speed * Time = 400 * (t - 0.5) = 400t - 200 (nautical miles)
Since the distance traveled by the second aircraft when it overtakes the first aircraft will be equal to the distance traveled by the first aircraft, we can set up the following equation:
300t = 400t - 200
Simplifying the equation:
200 = 100t
t = 2 hours
Therefore, the second aircraft will overtake the first aircraft after approximately 2 hours.
Considering that the second aircraft leaves at 09:30, the approximate time when it overtakes the first aircraft would be:
09:30 + 2 hours = 11:30
Since none of the given options match exactly, the correct answer would be:
D. None of the above
To solve this problem, we can use the formula:
Time = Distance / Speed
First, let's calculate the time it takes for the first aircraft to reach point B:
Time_1 = Distance / Speed_1
Time_1 = 1000 Nautical Miles / 300 Nautical miles per hour
Time_1 = 3.33 hours
The first aircraft reaches point B after approximately 3 hours and 20 minutes.
Now let's calculate the time it takes for the second aircraft to catch up to the first aircraft.
The second aircraft departs 30 minutes (0.5 hours) after the first aircraft, so it has a time disadvantage. Therefore, we need to subtract this 0.5 hours from the total time taken by the first aircraft.
Adjusted Time_1 = Time_1 - Time_disadvantage
Adjusted Time_1 = 3.33 hours - 0.5 hours
Adjusted Time_1 = 2.83 hours
Now, we can calculate the distance the second aircraft needs to cover to catch up to the first aircraft:
Adjusted Distance = Distance - (Distance_1 - Distance_disadvantage)
Adjusted Distance = 1000 Nautical Miles - (300 Nautical miles per hour * 2.83 hours)
Adjusted Distance = 1000 Nautical Miles - 849 Nautical Miles
Adjusted Distance = 151 Nautical Miles
Finally, we can calculate the time it takes for the second aircraft to cover the adjusted distance:
Time_2 = Adjusted Distance / Speed_2
Time_2 = 151 Nautical Miles / 400 Nautical miles per hour
Time_2 = 0.3775 hours
Convert the decimal part into minutes:
Minutes = 0.3775 hours * 60 minutes per hour
Minutes = 22.65 minutes ≈ 23 minutes
Adding this time to the departure time of the second aircraft:
Time of catching up = 09:30 (departure time of the second aircraft) + 0 hours 23 minutes
This is approximately 09:53.
Therefore, the second aircraft will overtake the first aircraft at around 09:53.
However, none of the answer choices provided match this time. Thus, the correct answer is D. None of the above.