An airplane travels 600 miles against the wind in 4 hours, and makes the return trip with then same wind in 2 hours. find the speed of the wind.

The speed of wind is 75 miles / hour

Step-by-step explanation:

Let's assume

speed of airplane is x miles /hour

speed of wind is y miles /hour

Against wind:

An airplane travels 600 miles against the wind in 4 hours

against wind means resultant speed will be less

so, speed =x-y

total distance traveled in 4 hour is

and this has to be equal to 600

Divide both sides by 4

and we get

With wind:

makes the return trip with then same wind in 2 hours

with wind means resultant speed will be more

so, speed =x+y

total distance traveled in 2 hour is

and this has to be equal to 600

Divide both sides by 2

and we get

So, we get system of equations

now, we can solve it by adding both equations

now, we can solve for x

now, we can  find y by plugging x into any one equation

So,

The speed of wind is 75 miles / hour

y=sec x is the correct answer

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