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dalia flies an ultralight plane with a tailwind to a nearby town in 1/3 of an hour. on the return trip, she travels the same distance in 3/5 of an hour. what is the average rate of speed of the wind and the average rate of speed of the plane? initial trip: return trip: let x be the average airspeed of the plane. let y be the average wind speed. initial trip: 18

User WoDoSc
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2 Answers

5 votes

Final answer:

To find the average rate of speed of the wind and the average rate of speed of the plane, we can use the concept of relative velocity. Let's assume the average airspeed of the plane as x km/h and the average wind speed as y km/h. By setting up and solving equations, we can find the values of x and y.

Step-by-step explanation:

To find the average rate of speed of the wind and the average rate of speed of the plane, we can use the concept of relative velocity.

Let's assume the average airspeed of the plane as x km/h and the average wind speed as y km/h.

On the initial trip with the tailwind, the plane covers a certain distance in 1/3 of an hour. So, the relative speed of the plane and wind is (x + y) km/h.

Similarly, on the return trip, the plane covers the same distance in 3/5 of an hour. So, the relative speed of the plane and wind is (x - y) km/h.

We can set up the following equations:

(x + y) = distance / (1/3) and (x - y) = distance / (3/5)

Solving these equations will give us the values of x and y, which represent the average rate of speed of the plane and the wind, respectively.

User Harshad Kavathiya
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7.9k points
5 votes

Dalia had an average airspeed of

42

miles per hour.

The average wind speed was

12

miles per hour.

User Activedecay
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7.6k points