The average airspeed of a single-engine aircraft is 150 milesper hour. If the aircraft flew the same distance in two hours with the wind as it flew in 3 hours against the wind, what was the effect of the wind on the plane? What are the equations? What is wind speed?

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30 mph

To find the effect of the wind on the plane, we first need to set up some equations. Let's denote the speed of the aircraft in still air as "S" and the speed of the wind as "W".

When flying with the wind, the effective speed of the aircraft is increased by the speed of the wind, so the equation becomes:

S + W = 150 miles per hour

When flying against the wind, the effective speed of the aircraft is decreased by the speed of the wind, so the equation becomes:

S - W = 150 miles per hour

Now, we are given that the aircraft flew the same distance in two hours with the wind as it flew in three hours against the wind. We can use the formula Distance = Speed × Time to set up two more equations:

Distance with the wind = (S + W) × 2
Distance against the wind = (S - W) × 3

Since the distance is the same in both cases, we can set these two equations equal to each other:

(S + W) × 2 = (S - W) × 3

Now, let's solve this equation to find the value of W, the speed of the wind.

Multiplying out the equation:

2S + 2W = 3S - 3W

Combining like terms:

3W + 3W = 3S - 2S

6W = S

Simplifying:

W = S/6

So, the equation for the speed of the wind is W = S/6.

To find the effect of the wind on the plane, we need to substitute an actual value for "S". Since we are given that the average airspeed of the single-engine aircraft is 150 miles per hour, we can substitute S = 150 into the equation:

W = 150/6 = 25 miles per hour

Therefore, the speed of the wind is 25 miles per hour. The wind is blowing at a speed of 25 miles per hour in the opposite direction of the aircraft's travel.