A bicyclist rides up a 10 mile hill at a constant speed of 10 MPH. He arrives at the top and heads down to the bottom at a constant speed of 30 MPH

What is his average speed for the round trip?

depends how long the down hill was...

I'll assume it's a perfectly symmetrical hill.

He rides up at 10MPH, so he takes an hour, he rides down at 30MPH, so he takes 20 minutes

so the average in time is \frac{(10*60)+(30*20)}{80}

or if you want the average over distance, it's \frac{10+30}{2}

I assume you want the time one, but you don't specify in the question.

does that make sense? It's speed for each section of time, weighted over the total time.

Please respond if you don't follow