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One airplane travels due north at 300 km/h, while another travels due south at 300 km/h . Are their speeds the same? Explain.

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Yes, the airplanes are traveling at the same speed of 300 km/h, one towards the north and the other towards the south. 

Speed is the ratio of distance traveled to time taken, or,

speed = distance/time

In the given case, the planes are moving at 300 km/h in different directions. One of the planes will travel 300 km towards north in 1 hour, while the other plane will travel 300 km towards south in the same amount of time. Using the relation between distance, time and speed, we can see that both the planes have the same speed (of 300 km/h).

However, if we are calculating the relative speed of planes (that is, how fast is one plane moving with respect to the other), then each plane is traveling at 600 km/h, relative to the other.

Hope this helps. 

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