Bob challenges Alice to a swimming race from one end of a 10-meter pool to the other. Bob is so confident he will win that he lets Alice use the starting block
because diving in from there will give her a lead. He will start in the pool at the wall.
Alice accepts the offer. At time t=0 seconds, Alice hits the water 2 meters out from
the edge of the pool at a constant speed of 1 meter per second, which she maintains
throughout the race. Meanwhile, at t=0, Bob starts off from rest at the pool wall
and is speeding up. Bob's distance from the wall at any given time, t, is given by
B(t)=0.25t”, where B(t) measures the distance from the starting point at the pool
wall. Will Bob be able to beat Alice to the opposite end of the pool? Is it possible for
Bob to win, and if so, how long would the pool need to be for him to win?