Which option correctly represents the formula for the critical point in a flight plan with distance D, outward speed O, and home speed H?

• A. (D*O)/(O+H)
• B. (D+O)/(O+H)
• C. (D*H)/(D+H)
• D. (D*H)/(O+H)

Answer: (D)

The key idea is balancing two different-speed legs of a flight to find where you should turn around. Imagine you turn around at a distance x from home. The time to fly back from that turning point is x divided by the home speed. The remaining outward distance to the target is D minus x, and if you kept going outward it would take (D − x) divided by the outward speed.

Set these two times equal to reflect the point where the return trip and the remaining outward progression would take the same amount of time:

x/H = (D − x)/O

Solve for x:

O x = H(D − x)

(O + H) x = H D

x = H D / (O + H)

So the turning point from home is HD/(O+H). This is why that option is the correct representation: it comes from equating the return-trip time to the time needed to complete the remaining outward distance under the given speeds.

If you were balancing a different pair of times (for example, outward time to the turn vs. return time), you’d get a different expression such as OD/(O+H), which corresponds to a different setup. Here, the problem’s wording leads to the HD/(O+H) form.