Q: At speeds of 200,400,600, and 800km/hr, an aeroplane files down the four corners of a square. Determine the plane's average speed as it circles the field.

The total distance traveled around the square is given as the sum of the distances traveled along each side. 

Since each side of the square is x km long and there are four sides, the total distance traveled is 4x km.

The total time taken to fly around the square is given as the sum of the times taken to fly along each side. 

Since the speed of the plane along each side is given, we can divide the distance traveled by the speed to find the time taken for each side. 

For example, to find the time taken to fly 200 km at a speed of 200 km/hr, we would divide 200 km by 200 km/hr to get 1 hour. 

Therefore, the total time taken to fly around the square is x/200 + x/400 + x/600 + x/800 hours.

To find the average speed, we can divide the total distance traveled by the total time taken. In this case, the total distance traveled is 4x km and the total time taken is x/200 + x/400 + x/600 + x/800 hours. 

Therefore, the average speed is 4x km / (x/200 + x/400 + x/600 + x/800) km/hr.

By substituting the values given in the problem, we can solve for y, which is the average speed. 

In this case, the average speed is y = (4x km) / (x/200 + x/400 + x/600 + x/800) km/hr. 

Plugging in the values given in the problem, 

we get y = (4x km) / ((x/200) + (x/400) + (x/600) + (x/800)) km/hr 

= (4x km) / (25x/2500) km/hr = (4x km) / (4x/y) km/hr = 

y = 2400*4/25 

= 384 km/hr.