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------------------------------------------------ Two helicopters take off simultaneously from airfields A and B, which are 500 km apart. After 1 hour and 20 minutes from their meeting point, the helicopter originating from airfield A lands at airfield B. The second helicopter lands at airfield A 3 hours after the meeting. Determine the speed of both helicopters.

The speed of the helicopter originating from airfield A is \[tex](375 \, \text{km/h}\),[/tex] and the speed of the helicopter originating from airfield B is[tex]\(250 \, \text{km/h}\).[/tex]

Explanation:

Let (x) be the speed of the helicopter from airfield A and (y) be the speed of the helicopter from airfield B.

The helicopter from airfield A travels for 1 hour and 20 minutes, covering a distance of[tex]\(1 \, \text{hour} \times x + \frac{1}{3} \, \text{hour} \times y\)[/tex], which is equal to the distance between the airfields. Similarly, the helicopter from airfield B travels for 3 hours, covering a distance of [tex]\(3 \, \text{hours} \times y\)[/tex], which is also equal to the distance between the airfields.

So, we have the equation:

[tex]\[1x + \frac{1}{3}y = 500\]\[3y = 500\][/tex]

Solving these equations simultaneously, we find[tex]\(x = 375 \, \text{km/h}\) and \(y = 250 \, \text{km/h}\).[/tex]

Therefore, the speed of the helicopter originating from airfield A is[tex]\(375 \, \text{km/h}\)[/tex], and the speed of the helicopter originating from airfield B is [tex]\(250 \, \text{km/h}\).[/tex]

In conclusion, by setting up and solving equations based on the distances covered by each helicopter, we determine the speeds of the helicopters from airfields A and B as [tex]\(375 \, \text{km/h}\) and \(250 \, \text{km/h}\),[/tex] respectively.