Answer to Question #162858 in Algebra for Ansy

Question

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, att 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 ^ 3 , 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?

Answer 1

the length of the pool is 10meter. $S_p$ = 10m;

Alice t = 0 $\to$ $S_o = 2m$ $v = 1\large\frac{m}{s}$

Bob t = 0 $\to S = \large\frac{t^3}{64}$

Alice: $t_1 = \large\frac{S - S_o}{v} = 8s$

for Bob: $S = (\large\frac{t}{4}) ^3$ $= \frac{512}{64} = 8m$

If the pool 10m The bob won't be won in competition because when the Alice arrive to finish The bob is 2m from the finish

2) $2 + 1* t = \large\frac{t^3}{64}$

$t^3 -64 t - 128 = 0$

S = 10.8m