A cyclist starts from rest and completes a $15\text{-mi}$ race in $45\text{ minutes}$. Suppose the cyclist's speed at the finish line is zero, explain why the cyclist must have been riding at exactly $20\text{ mph}$ at least twice during the race.

The cyclist must have crossed the average speed of $20\text{ mph}$ at least twice since the speed is always equal to the average speed at every moment during the race.

The cyclist must have crossed the average speed of $20\text{ mph}$ at least twice since the cyclist accelerates at the start past $20\text{ mph}$ and decelerates past it again to reach zero speed.

The cyclist must have crossed the average speed of $20\text{ mph}$ at least twice because maintaining a steady pace is required except at the start and finish.

The cyclist must have crossed the average speed of $20\text{ mph}$ at least twice because the speed increased linearly until the midpoint, then decreased linearly to zero.