An airplane takes 3 hours to travel a distance of 2250 miles with the wind. the return trip takes 5 hours against the wind. find the speed of the plane in still air and the speed of the wind.

Speed of Plane = 600 miles per hour

Speed of Wind = 150 miles per hour

Step-by-step explanation:

The distance equation is D = RT

Where

D is the distance

R is the rate

T is the time

Let rate of airplane be "x" and rate of wind be "c"

Also, note:  rate with wind is airplane's and wind's, so that would be "x + c"

and rate against the wind is airplane's minus the wind's, so that would be "x - c"

Now,

2250 miles with wind takes 3 hours, so we can write:

D = RT

2250 = (x + c)(3)

and

2250 miles against the wind takes 5 hours, we can write:

D = RT

2250 = (x - c)(5)

Simplifying 1st equation:

Simplifying 2nd equation:

Multiplying the 1st equation by 5, gives us:

Multiplying the 2nd equation by 3 gives us:

Adding up these 2 equations, we solve for x. Shown below:

Now putting this value of x into original 1st equation, we solve for c:

Speed of Plane = 600 miles per hour

Speed of Wind = 150 miles per hour

step-by-step explanation: