Question

an airplane travels from Atlanta to Tokyo, Japan, in 22 hours. The flight back takes 17 hours. The difference is caused by wind that blows primarily from west to east. If the airplanes average speed in still air is 550mi/hr, what is the average speed of the wind during the round trip flight? Round to the nearest mile per hour? Show Ur work.

Answer 1

Wind speed to Nearest mile = 71 mile per hour.

Explanation:

To solve this problem lets discuss basic concept of effect of wind speed on speed of any object.

If wind direction is same as that of object then speed of object will increase by amount the speed of wind.

If the speed of object in still air is X

and speed of air is Y

Then net speed of object in presence of wind will be X + Y

If wind direction is opposite to that of object then speed of object will decrease by amount the speed of wind.

If the speed of object in still air is X

and speed of air is Y

Then net speed of object in presence of wind will be X - Y.

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Given

Time taken from Atlanta to Tokyo is 22 hours

Time taken from Tokyo to Atlanta is 22 hours

Let the distance of Atlanta to Tokyo be D miles.

formula for Time is Distance / Speed

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Time taken from Atlanta to Tokyo is 22 hours

Distance is D

Speed of airplane = 550mi/hr

let the speed of wind be W mi/hr

Since speed of wind from Atlanta to Tokyo is in opposite direction as wind blows primarily from west to east and it can be also checked from the fact that it takes more time to from Atlanta to Tokyo 22 hours.

therefore

wind speed will be opposite to that of airplane

so net speed of airplane in presence of wind will be (550 - W)mi/hr

putting it in equation of time formula

22 = D/550 - W

=>D = 22 * (550 - W) ---------------> (A)

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Time taken from Tokyo to Atlanta is 17 hours

Distance is D

Speed of airplane = 550mi/hr

let the speed of wind be W mi/hr

Since speed of wind from Tokyo to Atlanta is in same direction as wind blows primarily from west to east and it can be also checked from the fact that it takes less time to travel from Tokyo to Atlanta 17 hours.

therefore

wind speed will be opposite to that of airplane

so net speed of airplane in presence of wind will be (550 + W)mi/hr

putting it in equation of time formula

17 = D/550 + W

=>D = 17 * (550 + W) ----------------> (B)

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As distance D will be same

equating equation A and B we have

22 * (550 - W) = 17 * (550 + W)

=>22* 550 - 22 W = 17* 550 + 17 W

=>22* 550 - 17* 550 = 17 W + 22 W

=> 550(22-17) = 39W

=> W = (550*5)/39

=> W = 2750/39 = 70.5218

Wind speed to Nearest mile = 71 mile per hour.