Average Speed of an Aeroplane

The average speed of an aeroplane can be calculated by using the formula:

Average speed = total distance / total time

Given information:

- The aeroplane flies from A to B at a rate of 500 km/hour.
- The aeroplane comes back from B to A at a rate of 700 km/hour.

To calculate the average speed, we need to find the total distance and the total time taken by the aeroplane.

Total Distance:

- The distance from A to B is the same as the distance from B to A because it is a round trip.
- Let's assume the distance from A to B is 'd'.
- So, the total distance covered by the aeroplane in the round trip is 2d.

Total Time:

- Let's assume the time taken by the aeroplane from A to B is 't1'.
- The time taken by the aeroplane from B to A is 't2'.
- So, the total time taken by the aeroplane in the round trip is t1 + t2.

Now, we need to find the values of 'd', 't1', and 't2'.

- Distance = speed × time
- Distance from A to B = 500 × t1
- Distance from B to A = 700 × t2
- As the distance is the same in both cases, we can equate them.
- 500 × t1 = 700 × t2
- t1/t2 = 7/5

We can assume any values for t1 and t2 as long as they satisfy the above equation.

- Let's assume t1 = 7 hours and t2 = 5 hours.
- So, the distance from A to B is d = 500 × 7 = 3500 km.
- The total distance covered in the round trip is 2d = 7000 km.
- The total time taken in the round trip is t1 + t2 = 12 hours.

Now, we can calculate the average speed of the aeroplane.

- Average speed = total distance / total time
- Average speed = 7000 / 12
- Average speed = 583.33 km/hour (rounded to two decimal places)

Therefore, the average speed of the aeroplane is 583.33 km/hour.

In this question distance is same so there will be formula of H.M.
HM: 2ab/a+b
=2*500*700/500+700
=70000/1200
=58.33