Aplane is traveling between city a and city b, which are 2000 miles apart. city a is due north of city b, and there is a strong, constant wind blowing due south. at constant speed, it takes a plane 5 hours to go from a to b with the wind at its tail, but 8 hours to go back when facing this headwind. what is the speed of the wind?

Speed of the wind is 75 miles per hour

Distance between two city = 2,000 miles

With wind time taken by plane = 5 hours

Against wind time taken by plane = 8 hours

Plane speed = a

Wind speed = b

So,

a + b = 2000 / 5

a + b = 400 eq1

a - b = 2000 / 8

a - b = 250 eq2

From eq 1 - eq2

2b = 150

b = 75 mile per hour

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The speed of the wind is 75 mph.

Step-by-step explanation:

Let the actual speed of the plane is x mph and that of the wind is y mph.

Therefore, the speed of the plane when it goes from A to B with the wind is at its tail is (x + y) mph and the speed of the plane when it goes from B to A facing the headwind is (x - y) mph.

Given that,  

............ (1) and  

............. (2)

Now, from equations (1) and (2) we get

2y = 400 - 250 = 150

⇒ y = 75 mph.

Therefore, the speed of the wind is 75 mph. (Answer)

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