## Jet Plane

A jet plane makes a round trip from Yarmouth to Sydney. When the plane is flying into a headwind during the trip, its speed is $300$ km/h, and its speed with a tail wind is $600$ km/h. What is the average speed for the round trip?
Source: NCTM Mathematics Teacher, December 2005

SOLUTION
Let $d$ represent the distance in kilometers from Yarmouth to Sydney. If we assume that the trip to Sydney is made up entirely of head wind and that the return trip is made up entirely of tail wind, then the roundtrip flying time equals
$\dfrac{d}{300}+\dfrac{d}{600}=\dfrac{3d}{600}=\dfrac{d}{200}$
The round trip average speed equals
$2d\div\dfrac{d}{200}=400$

Answer: $400$ km/h