Solution for #19

Alternate Solution #1

Let s be the total distance of the journey to the hotel. Let v be walking speed. So 2v is the bike's speed, and 8v is the train's speed. Let I be the time it took for Isaac to complete the journey, and A be the time it took for Albert to complete the journey. Since distance equals rate times time, we have two equations, one for I and one for A:

        I = (s/2)/8v + (s/2)/v = s/16v + s/2v
        A = s/2v 

Note that I exceeds A by s/16v. Albert will reach the hotel first.

Alternate Solution #2

The problem may be solved more easily with simple logic. If the bicycle is twice as fast as walking, the time it takes to bike the whole way is equal to the time it takes to walk half the way. So if the train's speed is anything shy of infinite, biking will still be faster.