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With a head wind, it takes 7 hours to fly 2800 miles from miami to seattle. with a tailwind, and the same airspeed, it takes 5 hours to fly in the opposite direction, from seattle to miami. find the airspeed and the windspeed

 Feb 4, 2020
 #1
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2800 / 7 = 400 mph - its speed from Miami to Seattle

2800 / 5 =560 mph - its speed from Seattle to Miami

 

[560 + 400 ] / 2 =480 mph - its speed in still air.

[560 - 400 ] / 2 =80 mph - the speed of the wind.

 Feb 4, 2020
 #2
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+1

Call the windspeed,  W

Call the rate of the plane in still air, R

 

And

 

With the wind the effective rate  is R + W

Against the wind the effective rate is R - W

 

And  we know that   distance / rate   = time  ....so....

 

2800 / (R + W)  = 5           2800 / (R - W)  = 7

2800 = 5 (R + W)              2800 = 7 (R - W)

2800 / 5  = R + W              2800/7= R - W

560 = R + W                       400 = R - W

 

Add the last two  equations and we get that

 

960 = 2R

480  = R

 

And

560 = R + W

560 = 480 + W

80  = W

 

 

cool cool cool

 Feb 4, 2020

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