A plane flies 910 miles with the wind in the same time it can go 660 miles against the wind. The speed of the plane is still air in 305 miles per hour. What is the speed of the wind?

If the plane flies with the wind, the speed will be the speed of the plane + the speed of wind. Since it can fly 910 miles, and the speed of the plane is 305

910 = (305 + w) x time (1)

If the plane flies against the wind, the speed will be the speed of the plane - the speed of wind. Since it can fly 660 miles, and the speed of the plane is 305

660 = (305 - w) x time (2)

Since the time is equal for both equation in 1 and 2:

[tex]\frac{910}{305+w}[/tex] = [tex]\frac{660}{305-w}[/tex]

→ 910(305-w) = 660(305+w)

→ 277550 - 910 w = 201300 + 660w

→ 1570w = 76250

→ w = 48.56

raphealnwobi raphealnwobi · Answer 2 · 2021-12-28T12:56:42+01:00

The speed of the wind is 48.6 miles per hour

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let a represent the speed of the wind, Let the time taken to cover the distance as t, hence:

a + 305 = 910/t

t = 910/(a + 305) (1)

305 - a = 660/t

305 - a = 660/(910/(a + 305))

305 - a = 0.72a + 221.2

a = 48.6 miles per hour

The speed of the wind is 48.6 miles per hour

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