An aeroplane flies at 800km/h for one third of its flight time and averages 700 km/h for the entire trip. What is the average speed, in kilometres per hour, over the remaining part of the journey?
A. 600
B.750
C.650
D.500
E.625
Could you please explain in detail thank you
distance=speed*time
So, if it flew at 800km/hr for x hours, then it flew at some unknown speed s for 2x hours:
800x + s*2x = 700*3x
800+2s = 2100
2s = 1300
s = 650
To solve this question, we can use the formula for average speed:
Average speed = Total distance / Total time.
Let's assume the total distance traveled by the airplane is D km and the total time taken for the trip is T hours.
It is given that the airplane flies at 800 km/h for one-third of its flight time. Therefore, the time the airplane flies at 800 km/h is (1/3)T hours. During this time, the airplane covers a distance of (1/3)T * 800 = (800/3)T km.
The remaining part of the journey is the time the airplane flies at the average speed of 700 km/h. This means the remaining time is T - (1/3)T = (2/3)T hours.
Now, we can calculate the remaining distance using the average speed formula:
Remaining distance = Average speed * Remaining time
= 700 km/h * (2/3)T
= (1400/3)T km.
To find the average speed over the remaining part of the journey, we divide the remaining distance by the remaining time:
Average speed = Remaining distance / Remaining time
= (1400/3)T km / (2/3)T h
= (1400/3) km/h.
Therefore, the average speed over the remaining part of the journey is (1400/3) km/h, which is approximately equal to 466.67 km/h.
None of the given options match this value exactly. However, option D (500 km/h) is the closest option to the calculated value.
To find the average speed over the remaining part of the journey, we first need to determine the time taken for the remaining part and the distance covered during that time.
Let's assume the total distance of the journey is d km.
We are given that the airplane flies at a speed of 800 km/h for one-third of the time. This means it flies at 800 km/h for (1/3) of the total time. So, it covers a distance of (800 * (1/3)) km during this time.
Now, let's calculate the remaining distance and time for the remaining part of the journey.
The average speed for the entire trip is given as 700 km/h. The total time for the trip can be found by dividing the total distance (d) by the average speed (700 km/h). So, the total time taken is (d/700) hours.
We already know that for one-third of the time, the airplane flies at 800 km/h. So, the remaining time for the flight is (2/3) of the total time.
The remaining distance can be found by subtracting the distance covered during the first one-third of the flight from the total distance. So, the remaining distance is:
d - (800 * (1/3))
To find the average speed over the remaining part of the journey, we divide the remaining distance by the remaining time:
(Remaining Distance) / (Remaining Time)
= (d - (800 * (1/3))) / [(2/3) * (d/700)]
Simplifying the equation:
= (d - (800/3)) / [(2/3) * (d/700)]
= (3 * d - 800) / [(2/3) * d]
= 3 * (3 * d - 800) / (2 * d)
= (9d - 2400) / (2d)
This expression represents the average speed over the remaining part of the journey.
To find the answer, we substitute the given values into the equation.
Without the specific distance value, we cannot determine the exact average speed. Hence, the answer cannot be determined.