# Speed of a Plane

On a recent flight from Phoenix to Kansas
City, a distance of 919 nautical miles, the plane arrived
20 minutes early.On leaving the aircraft, I asked the captain,
“What was our tail wind?”He replied, “I don’t know, but our
ground speed was 550 knots.” How can you determine if
enough information is provided to find the tail wind? If possible,
find the tail wind. (1 knot = 1 nautical mile per hour)

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### The get the distance, you can

The get the distance, you can multiply its speed by the time the plane traveled:

$$d = \frac{v}{t}$$

Then the total distance traveled by that plane is the distance traveled by plane without the tail wind and the distance traveled by plane with the tail wind, symbolized as...

$$d = \frac{v}{t} + v(t - \frac{1}{3})$$

We know that total distance traveled by plane is 919 nautical miles and the speed of the plane used to get there is 550 nautical miles. We now plug in those values, becoming:

$$919 = 550(t) - 550 (t - \frac{1}{3})$$

Getting the $t$, the value would be 1.15 hours. That is the total time the plane actually took to cover 919 nautical miles with the tail wind.

So what might be the value of this tail wind? Remember that the equation above is
the total distance traveled by that plane is the distance traveled by plane without the tail wind and the distance traveled by plane with the tail wind, symbolized as...

$$d = \frac{v}{t} + v(t - \frac{1}{3})$$

so....

$$919 = 550(1.1523) + 550(1.1523 - 0.66666667)$$
$$919 =633.765 + 267.0983$$

Notice that the value 633.76 nautical miles is the distance a plane could travel if there was no tail wind while the value 297.10 nautical miles is the additional distance a plane could travel when it got hit by a tail wind.

The value of this tail wind would be:

$$v = \frac{d}{t}$$

Then plugging in on values:

$$v = \frac{267.10}{1.1523}$$

$$v = 231.80$$

The tail wind would be a very fast 231.80 nautical miles per hour.

Hope it helps....:-)

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