A train flies round trip at a distance of X miles each away. The velocity with the head wind is 160mph, while the velocity with tail wind is 240mph, What is the average speed for the round trip?

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To get the average speed for the round trip, recall that...

$$distance = (speed)(time)$$ $$d = vt$$

We also know that $$average \space speed = \frac{total \space distance}{total \space time}$$

With that in mind...

The time required by train (a flying train, I suppose, hehe) to reach its destination is $\frac{X}{160}$ hours. The time required by train to return from its destination is $\frac{X}{240}$ hours.

So...

The total distance for the round trip would be $X+X = 2X$ miles.

The total time spent flying would be $\frac{X}{160}+\frac{X}{240} = \frac{X}{96}$ hours.

Therefore, the average speed for the entire round trip would be $\frac{2X \space miles}{\frac{X}{96} \space hours}$ = $\color{green}{192 \space miles \space per \space hour}$

Alternate solutions are encouraged...