Question

A bike drove 30 miles during a one hour trip. Show that bike speed was equal to 30 mile / hour at least once during the trip.

Answer 1

Let bike speed is less than 30 mile / hour during a one hour trip. Then the a bike drove less than $30 mile/hour\times1hour=30miles$ during a one hour trip. We have a contradiction.

Now suppose that bike speed is greater than 30 mile / hour during a one hour trip. Then the a bike drove greater than $30 mile/hour\times1hour=30miles$ during a one hour trip. We have a contradiction.

Therefore bike speed was equal to 30 mile / hour at least once during the trip.